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As I was considering returning to the Catholic faith, more than one month I go I decided to confess. Because I was in a long time without confessing, and also returning to the faith, I think he did a great job as a confessor. I was still doing some research about some topics (mainly about the liceity of the New Mass), so I didn’t go to Mass during this period. As a came to the conclusion that I was sinning by not going to Mass, and also because I wanted to receive the Eucharist, I decided to confess again. But this time he didn’t give me the same attention. He told me there was no need to confess again in such a short period of time things he considered to be venial sins, like the Skipping the Sunday Obligation and masturbation, which I disagree. He did absolve me from my sins but he was in a hurry so he didn’t wait me to tell all the things I wanted to confess.

So, first of all, was the absolution valid?
I feel like I’m not comfortable to receive the Eucharist and not comfortable to confess with him again.

He is the only priest in the city that is available for confession, as far as I know.

Use this as your primary resource to study the new "mass". Do not go to it for any reason, you do not fulfill your Sunday Obligation by going to it. Go to or call one of these places (SSPX) or hopefully someone will post other links to a resistance or other traditional Mass in your area where you can get the True Mass and sacraments. Or do a search in your area for the Traditional Latin Mass, strive to go to one that is non-diocesan. 

Do not go to diocesan confession, all sincere souls who go there ask the same question as you - "was the absolution valid?" The answer is - doubtfully at best, or no one knows.

From this comment alone, I have to believe the priest in question is a Novus Ordo priest.  If so, your confession was not valid.

Yep.  I would seek a Traditional priest and start all over with a General Confession.  Of course, the SSPX priests are instructed to tell you that the Novus Ordo Sacaraments are valid, so if you mention this to him, he might waive off re-confessing those sins.  But just say you want to make a General Confession, having been away from the Church long.  In a General Confession, you need make no mention of previous Confessions (unless there's a need to confess having concealed something during one of those).