Teething/Hairball Question

Just a quick question ... Apart from using mums toes and fingers as teething toys .. can vomiting also be a part of teething as in babys?

Nothing really comes up when he heaves, just makes the noises and a bit of bile, then he goes and eats. He's done this twice today.
(Which leads to mum scrubbing a white carpet! That stuff stains bad lol)
Other then that, he's normal.

He now has 4 adult teeth thru in a week! (Baby ones still in place) So I suspect is feeling a bit sore.

I have been reading about teething/vomiting posts on here, and also maybe another possibility is a hairball?
I have never seen one before and don't really know what to look for?
Is dry heaving a symptom of it?

Kittens are a learning curve! Something new everyday!

Thanks in advance!

I would go see a vet. I have a cat who does that and she has hairball problems, asthma, and also recently had a blockage. I would guess hairballs but would get it checked it out incase it is something more serious.