What could this lump underneath my right rib cage be?

Depends on : Depends on how long it has been there, whether it is hard, or soft, painful or painless, and other. Get it looked at if new onset over several months or less.

Several things: Problems like these can only be correctly handled by your doctor in person. He/she needs to listen to you, perform an examination and possibly run labs or other tests. That's the only way he/she can find out what's going on and what to do about it.