It is certainly possible to have pain in this part of your hand from a number of causes. Probably the most common cause is a tendonitis, which is an inflammation in the tendons where the attach to the muscles in the hand. This injury
is usually from repetitive motions involving the hand, such as typing at a keyboard.
In addition to tendonitis, it is also possible to pull or strain the muscles in the hand themselves, although this is less common. Symptoms would be similar to tendonitis.
Finally, if you accidentally banged your hand or some other similar injury, it could be possible to have an area of bruising or contusion
causing the pain. Once again, symptoms would be similar to either a pulled muscle or tendonitis, although there may also be an area of visible bruising.
It would be worthwhile to see your primary care doctor
about this pain, especially if it is persistent or not improving. They will be able to examine the hand and help you figure out exactly what is going on. Furthermore, they can give you some advice on which medications you might want to take to help reduce the pain and speed healing.