I had asked for some additional information and have not heard back.
There are several common causes of tender bumps on the hand. There are several types of bumps that are similar, in that they are related to underlying musculoskeletal inflammation, such as of a joint or a tendon. There are also some bumps that can develop in the skin that can be tender.
I asked about more details of the location of the bump in the hand, as he location can help to guide the most likely cause of the bump at that location.
Without more specific information regarding location, the best advice that can be given would be the use of paracetamol, a trial of an oral anti-inflammatory medicine and/or the local application of moist heat. The paracetamol does not treat inflammation, but has far fewer side effects. There are a couple of anti-inflammatory medicines available over the counter, but naproxen is generally better tolerated int he elderly. Even with the naproxen, though, we would rather use anti-inflammatory medicines for the least amount of time to get control of the problem. Moist heat has an anti-inflammatory effect, and also has the advantage of being well tolerated.
If I can provide any additional information, please let me know.