I wouldn't dare diagnose someone's condition over the net. The first thing I would check is your action. The other thing is, a bari may just be too much uke. I can't play one at all, except for the B and E strings. There are exercises you can do to strengthen the pad of your thumb, you might consult an occupational therapist.
According to Craig Chee you should not be able to see your thumb from the front of the uke, the whole thumb is supposed to rest (grab) lengthwise along the back of the neck, in most cases.
Surgery can help a lot of things, but that's always a last resort. I have hand pain at times, it feels like I'm being stabbed, but if I take my daily dose of turmeric it helps a lot. Just sayin....
Keep us posted. And good luck!