Agree - eye problems can be really quite painful and it needs a vet visit - but do see an exotic vet who knows about eye problems. I had eye issues with our previous syrian and he was too old for surgery, so it was a case of keeping him comfortable on metacam as long as possible. I don't think a vet would suggest having him pts unless they decided it was a tumour pushing the eye out possibly. And even then they may say - see how he goes on metacam for a while. Does he seem fine in himself? They can also prescribe eye drops so the dry eye doesn't cause too much discomfort,
From what I've learned with eye issues, your hamster is likely to already be blind in that eye. Once it goes dry it's probably a "dead eye". It doesn't matter - they can't see that well anyway and he can manage fine with one
I found our hamster started running the other way round in his wheel (ie with his good eye pointing outwards).
It could be anything from an abscess to a tumour and probably the first thing they will try is antibiotics - to see if it goes down again. As well as metacam for pain relief and possibly eye drops.
The other thing - just to prepare you for the possibility. The dead eye could fall out under certain circumstances - not as bad as it sounds!