The grammar is fine, but the tone is very formal. I would suggest: I've started drawing recently, even though I didn't use to like it. It seems that I now enjoy doing lots of things that I never used to like to do.

It is good. Rather than "the things which", perhaps you meant to say "some things that". It's not wrong but the precision of "the things which" it makes it sound like you have taken to ALL of the things you didn't like before, which would be hard to believe.