Good deeds and acts of necessity are not forbidden on the Sabbath. It is meant as a day of rest, worship and recreation. You can do very little of these things under the burdensome yoke of the Pharisees, which is why Our Blessed Lord rebuked them.

The words of Our Lord in the Gospel of St. Matthew, chapter 12, addressed this concern of the OT laws of the Sabbath:

[1] At that time Jesus went through the corn on the sabbath: and his disciples being hungry, began to pluck the ears, and to eat. [2] And the Pharisees seeing them, said to him: Behold thy disciples do that which is not lawful to do on the sabbath days. [3] But he said to them: Have you not read what David did when he was hungry, and they that were with him: [4] How he entered into the house of God, and did eat the loaves of proposition, which it was not lawful for him to eat, nor for them that were with him, but for the priests only? [5] Or have ye not read in the law, that on the sabbath days the priests in the temple break the sabbath, and are without blame?

But I tell you that there is here a greater than the temple. [7] And if you knew what this meaneth: I will have mercy, and not sacrifice: you would never have condemned the innocent. [8] For the Son of man is Lord even of the sabbath. [9] And when he had passed from thence, he came into their ѕуηαgσgυєs. [10] And behold there was a man who had a withered hand, and they asked him, saying: Is it lawful to heal on the sabbath days? that they might accuse him.

[11] But he said to them: What man shall there be among you, that hath one sheep: and if the same fall into a pit on the sabbath day, will he not take hold on it and lift it up? [12] How much better is a man than a sheep? Therefore it is lawful to do a good deed on the sabbath days. [13] Then he saith to the man: Stretch forth thy hand; and he stretched it forth, and it was restored to health even as the other. [14] And the Pharisees going out made a consultation against him, how they might destroy him. [15] But Jesus knowing it, retired from thence: and many followed him, and he healed them all.

Furthermore, St. Mark 2:27:

And he said to them: The sabbath was made for man, and not man for the sabbath. [28] Therefore the Son of man is Lord of the sabbath also.

The Catholic Encyclopedia on the matter:

Christ, while observing the Sabbath, set himself in word and act against this absurd rigorism which made man a slave of the day. He reproved the scribes and Pharisees for putting an intolerable burden on men's shoulders (Matthew 23:4), and proclaimed the principle that "the sabbath was made for man, and not man for the sabbath" (Mark 2:27). He cured on the Sabbath, and defended His disciples for plucking ears of corn on that day. In His arguments with the Pharisees on this account He showed that the Sabbath is not broken in cases of necessity or by acts of charity (Matthew 12:3 sqq.; Mark 2:25 sqq.; Luke 6:3 sqq.; 14:5). St. Paul enumerates the Sabbath among the Jєωιѕн observances which are not obligatory on Christians (Colossians 2:16; Galatians 4:9-10; Romans 14:5). The gentile converts held their religious meetings on Sunday (Acts 20:7; 1 Corinthians 16:2) and with the disappearance of the Jєωιѕн Christian churches this day was exclusively observed as the Lord's Day.

I believe the Catechism of St. Pope Pius X does a good job of overviewing the expectations and prohibitions of the Sabbath day:

6 Q. What does the Third Commandment forbid?
A. The Third Commandment forbids servile works and any other works that hinder the worship of God.
7 Q. What servile works are forbidden on festivals?
A. The servile works forbidden on festivals are those works called manual, that is, those material works in which the body has more part than the mind, such, for instance, as are ordinarily done by servants, labourers, and artisans.
9 Q. Is no servile work permitted at all on festivals?
A. On festivals those works are permitted which are necessary for life, or for the service of God; as well as those done for a grave reason, with leave, when possible, from the Pastor.
10 Q. Why is servile work forbidden on festivals?
A. Servile work is forbidden on festivals in order that we may the better attend to divine worship, and to the care of our souls; And to enable us to rest from toil. Hence innocent recreation is not forbidden.
11 Q. What else above all should we avoid on festivals?
A. We should above all avoid sin and whatever leads to sin, such as dangerous diversions and dangerous places of amusement.

As you can see, it is not a day to be meticulously, and scrupulously, trying to avoid any necessary labors whatsoever. The rigorism of the OT Law is not at all applicable to what was given by the Lord of Sabbath Himself and His Church under the NT Law.

This gets dangerously close to scrupulosity.

The Church is not unreasonable about Sunday work, least of all when it is necessary.  On a personal note, while I am in a caregiving situation where schedules can change on a moment's notice, and I may be called upon 24/7 to tend to my father's corporeal needs, this said, I have recently begun to re-assess "what is necessary on Sunday and what isn't", especially regarding shopping.  I do not do this as a scruple, but rather, to put things to rights in regard to "shopping creep" and "work creep" that is far too easy to let sneak up on oneself.  My father's dietary supplements from Walmart are necessary, buying a Blu-Ray DVD player is not.  (I held off on buying the Blu-Ray until after midnight on Sunday, when I then placed the order on the Best Buy website and picked it up on Monday.)  Again, no scruple here, just resistance against letting Sunday gradually become "just another day", and against "feeding the beast" of a secular, apostate economy and social system that only remains profitable on Sundays if we let it happen.

I have attached what Jone has to say about it in Moral Theology.  He is actually on the strict side --- I know he was writing in the 1920s, and my edition has a 1961 imprimatur, but his observations, for instance, about operating an automatic washing machine are a bit antiquated, with power dryers having become commonplace, hanging clothes out to dry is now a quaint throwback, at least in Anglophone (and Francophone) North America, and merely dumping clothes into the washer, adding detergent, and pressing a button, to object to those things, taken all by themselves, would be almost тαℓмυdic.  I would say, in all cases, use common sense informed by a sensus catholicus.  If I am going to Walmart to get my father a box of generic Ensure equivalent, then get there and remember that we're low on orange juice and eggs, I'm not going to get a scruple and say "I have to wait till tomorrow to come back and get those other things".  Again, common sense.  If in doubt, consult a traditional confessor.