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At this age they want to explore and experience. I second Mater’s idea of toy bins.

Have sensory boxes. They don’t have to be big, even shoe box size will work. Have one with sand and some toys to scoop around sand with. Have one that you can fill with water and have some toys that float to go with it. Have one box with blocks that they can build with. Another will fun objects that feel different. Alternate the boxes as Mater said.

At this age it is ok to insist upon some independence from your little one. Put a baby gate up between her and the room you are working in. She will pitch a fit at first. You will need to be firm and it will be difficult for you.Even just 30 minutes will give you time to get something done then you can snuggle with them again.

Also it’s not the end of the world to let your kid watch a show for awhile.

If you only have one child, it is HARD. With only you to entertain them, it is difficult to accomplish what you’d like.  Lower standards if you need to as long as the King of the house is satisfied with it. My husband is generally happy with the house as long as I am not stressed about it. As long as everyone gets fed, educated and nurtured, he has clean clothes for work and the kids don’t mess up our bed or leave stuff in our room, he is pleased.

Asking for someone else:

I’m having a very hard time getting household duties done due to the constant interruption of my 33 month old daughter. I have no help and there is no one else in the house so all she has is me, so of course she’s chasing me around all day and now all she wants to do is play all the time. Of course there’s no one else to play with so she wants me to play with her.

I have a timer I set to play with her for a little while and tell her I’ll go do X whenever it beeps and she’s been having meltdowns all the time now. It used to be better but lately it hasn’t. She’ll start crying and asking to nurse (she’s still nursing) and won’t stop until I nurse her.

The longest I have ignored her is about 20 something minutes but I know they can go on crying for hours on end. It’s incredibly hard to be listening to the non stop crying and at the same time try to do things.

I don’t want to give in to just putting a video and make her be on screens all the time. At the same time I don’t want to be listening to her crying non stop for hours.

I’ve also tried to incorporate her into as many things as possible but this can’t be done for everything.

Is this just how it is now? Prioritize anything that is a strict necessity (like food) and all the rest, leave it to be accomplished at a snail’s pace?

I agree with Mithrandylan.  Since the child is almost 3 years old, she really should be weaned.  Giving her a bottle of milk while you work in the kitchen or are folding laundry might help to distract her temporarily as well as good toys like Jen51 and Mater suggested. 

I also want to mention that the best way to help a child get over being so clingy and winey is to have another child to replace her as "the baby".  If you aren't able to have more children for some reason, maybe find a someone's child to watch for them and to be a playmate for her.  

A little crying is good for children as it teaches them patience and that they won't get everything that they want.

That being said...  I have found that with 4 little boys 7 and under (baby is almost 1 and need a lot of attention) that sometimes I have to work in 15-30 minutes intervals with breaks to give them attention or help them with something.  Start a load of clothes to be washed and load the dishwasher and then take a break.  Clean up one room and then take a break.  Make breakfast and then take a break.  Clean up after a meal and then take a break.  Do schoolwork  with the 2 older boys and then take a break (our toddler is usually on my lap for this screaming or attempting to draw). 😅

There is rarely a day that I go to bed that the house is fully "cleaned up" but we do generally have a happy house.  Everyone has clean clothes and is well-fed with home-cooked food.

Sometimes you have to figure out what is most important and pick which things you can get done in a day.

On a final note, I was thinking again at how your little one is almost 3 years old.  Our 3rd child went through (Actually he is still going through) the "terrible 3s".  Instead of the terrible 2's he started going through something similar a little bit before he turned 3 (this past February).  If he doesn't get what he wants he screams, throws himself on the floor, says things to try and make people mad etc.  Usually when he does this I quietly remove myself from the room to show him that his anger will not be rewarded.  If his temper tantrums are very bad, we place him in a room by himself until he stops screaming.  The episodes have gotten fewer and fewer the more he learns that he will be ignored and isolated whenever he acts in this manner.

Prayers for you and the little one.  Disciplining children and balancing homework can be difficult.  But the reward is worth it.