TromboneChat

So I noticed that when I play, the part lips of my lips that aren't in the mouthpiece push out slightly, no air leaks through though. Is this a big deal, and how should i approach fixing it if so?

It's impossible to make a judgement without seeing it.
But it sounds to me like it's probably OK. A lot of players look like that.
Are you having playing problems, or just noticing how it looks?

I’m just noticing how it looks, I sound better than ever. Just wanted to make sure it wouldn’t be a thing that would haunt me down the road

Put your mind at rest, have a lesson with DE!

Smile embouchure could be a problem, but if you can play any register successfully probably it's just how your embouchure looks.