What do I do about hard bumps under the skin in my hands? Also my pinky finger is bending downward. What to do?

Dupuytrens. Dupuytren's contracture. It is usually a painless contracture / bending of the finger(s). http://centraljerseyhand.com.
May be Dupuytren's. Sounds like you may have dupuytren's disease. It is a benign condition that, as it progresses, causes the finger(s) to contract down towards the palm. There are several treatments, including a new, non-surgical injection. The best thing to do is to see a hand surgeon to confirm the diagnosis and discuss treatment options. If the contracture is not severe, then observation may be recommended.
Dupuytren's Disease. Sounds like dupuytren's disease, which is a benign, often progressive disease that can run in families. It causes the soft tissues under the skin to coalesce and form nodules and cords. It usually effects both hands and can cause the fingers to curl into the palm. There are a variety of treatment options depending on the severity, but treatment is more successful before it progresses to far.
Popes disease. This sounds like something called dupytrens contracure which causes a thickening of tissues in the palm of the hands and can cause the fingers (usually the ring and little) to bend down to the palm. Can cause lumps in palm. Not cancer but usually requires injections or surgery to treat.
Dupuytren's. This is dupuytren's contracture. Check out assh.Org, or do your own web search for more info. Too much to go into here. If your finger is bending down from it, then you need to have it fixed. It can be fixed by surgery or sometimes an injection that can break the cord pulling the finger. Search for "xiaflex".