[souffle]

I'm sorry your hammy is so poorly. He is quite old for a hammy and at this age their immune systems are not so good and they tend to get infections.
That looks like a nasty infection there and it could be an abcess or even a tumour that is breaking down. I would take him to the vets and see what they say. It may be treatable with some antibiotics or it may be that he is in pain and you have to make a decision based on your love for him. I hope he can be seen very soon x