Neverwouldhaveguessed has given you some wonderful advice and, as a whole, I would tend to agree with it.
I do have one or two concerns though ...
He also told me today that he doesn't really want to deal with ANY of my problems ever - he just doesn't want to, doesn't think he should have to.
I'm sorry, but imho that is just not good enough. You shouldn't have to live in an emotional vacuum when it comes to your marriage. Relationships are a two-way street. Sometimes he will need your support. Other times you will need his. That's just the way things are (well, in my world at least).
but then again my problems are often trivial, incessant, and unexpected
Please don't invalidate all of your problems. If they mean something to you at the time, then they are important.
By all means, take that fitness class. Go out and make supportive friendships. It will benefit you as an individual, and it will benefit your marriage.
However, please do not think that everything is all your fault all of the time. It's not! Sure, in the extremely rare occasion problems in a relationship may be all one person's fault, but the majority of the time that is just not the way it is.
Take care and have a great time at that fitness class.