Had my gallbladder removed on 4/3/14. When I inhale, I feel a sharp pain where my gallbladder was. Doesn't hurt if I put pressure on it. What is it?

Hard to say. . There is no date in your question so hard to know how long it's been. 3 years ? If it's been a while see your surgeon to discuss. Neuromas, scar pulling in muscle, clips could all in theory cause pain but pretty unusual. If bad, see your surgeon .
Please see below. It sounds like a condition called atelactasis (collapse of a small part of lung) due to operative procedure. You should get one equipment called incentive spirometry to blow out and open up the lung units collapsed. If this does not help along with pain pills, you should see your surgeon.