You sound just like me. I'm also 20 with SI and ED.
I have told my parents about this stuff because it's been a problem since I was 14.
My dad makes jokes when he feels awkward or doesn't know what to say. It doesn't make what your dad said right, but it can help you understand. One of the best things I ever did was to talk to my dad about this. If I was you I would say "Dad, I'm sorry if I make you worry about me and that I haven't been very good with communicating with you, but I would really appreciate it if you could try not to make hurtful remarks about what I struggle with"

Communication is important because parents get really scared when their kids struggle with this sort of problem. They don't understand or know what to do. Some family therapy might help...

Anyway, I'm sorry that you had to go through this and are struggling. It's really great that you did tell your parents about ED - well done!!