How to ask for a psychiatrist?

*THIS IS NOT ME ASKING FOR A DIAGNOSIS! *

Keeping it simple, I finally got a doctor's appointment to talk about my intrusive thoughts, and she was really nice! Absolutely lovely and understanding. As a general physician, she didn't do a concrete diagnosis beyond ocd-esque thoughts and anxiety and can't really do much besides prescribe meds which makes sense, but I was wondering if I should ask to see a psychiatrist for a concrete diagnosis of anything.

Mostly, I want to know if it's OCD, anxiety, both or neither?? just so I know what kind of therapies I should be looking for. I don't really want meds, I'd rather do therapy to get strategies to deal with it, but I know therapies for OCD and anxiety are different.

I'm also just curious on which it is, or if it's neither and just OCD tendencies or anything. I feel really bad taking meds for something I don't have, I guess?

I feel bad asking though because she's so nice and understanding it feels like im chasing a diagnosis or disregarding what her advice is, but I'd still like more clarification on it. Would it be ok to ask for a psychiatrist? How would you go about asking to see specifically a psychiatrist (I'm Canadian in ON, btw)? I know waitlists are long too so I wouldn't want to clog it or anything, I guess, and if it's really just bad intrusive thoughts but not enough for a diagnosis for either, I'd feel so, so bad for wasting their time. idk.