I am an immigrant and an engineer but I still like to go out and socialize only with the right crowd..

A little background about me, I am an asian immigrant came to US at 17. I am 36 now and have a successful career. Being an immigrant with accented english and having an engineer carreer is definitely the worst combination that you can imagine for a person who naturally enjoys social interactions. I think I am a confident extrovert but growing up with broken English and constantly being in my head at work converts me to a shy introvert when I am uncomfortable.

Most people in my situation are already married to other immigrants and staying at home all day so they don't even need to worry about those. But I am different. I like Americans and I live like Americans. I also have a lot hobbies. Sometimes I still feel so mentally drained when I went out. Don't get me wrong, I still have fun but I expect more from myself so I don't have to replay those little awkward soical moments for hours in my head afterwards. And sometimes my anxiety gets so deep that I zone out for a brief moment like what I did in my social dance class.

I decide to see a therapist for my anxiety but how do I overcome my social skills and imperfect English ?