To me it doesn't look like ich, it looks like fin rot/fungus. Do you have other fish in there too? Because the missing piece on the top fin looks like a bite.
What tank size, what are the water parameters, and what other fish are in the tank?
Is his eye popped out too, or is that just how those fish are?
Well, I think it is either fin rot or fungus, or both, (probably both by the looks of it). And the best way to cure fin rot is clean clean water, and to get rid of the fungus, you need to get some Melafix or a similar product, (I am not sure where you are located).
How often do you change the water out, and how much?
And someone correct me if I am wrong, but isn't 15G too small for either one of those fish? If the tank is too small, you are going to be battling problems forever with them.
Most people on here change their water once a week, it is better for the fish that way. I change 50% of my tanks water every Sunday (5 tanks) And from not having his water changed, that probably led to fin rot, and then those sores got fungus. So yes, I would start changing more of the water, and get some anit-fungal medicine at the pet store.
Remember that the 20G you are thinking about using will not be cycled either, and as far as I know, oscars are pretty messy, so you would be changing part of that water out every day.