Glad you are here and sharing. so sorry about all the medical stuff- I have found that personally as well as what I hear from most folks is that we all suffer from things that are often directly connected to our drinking (and certainly, indirectly).
Here's something you said that is the crux of it for me:
"Not sure whether to see a psych, stop drinking and see if this goes away or maybe both."
I'd flip that to stop drinking, then see a psych/counselors/go to AA...and be proactive. ANY health issues can only be helped (not saying cured) by sobriety. Everything in your life? That too, and far more than you might even imagine now.
Take care and hope you stop drinking.