I had a similar bump on my hand with a black dot in it, a few years back and it was a wart. My daughter has also had a couple of them as well. I had mine removed by my physician but used the liquid wart remover on my daughter the first time and then used the medicated disks the second time. When a wart starts to get better it is important to keep putting the medicine on it to clear it completly up. Otherwise, it will come back. My sister found this out when she had one removed by her doctor and he didn't get all of it- the wart came back. Also to note that as the wart does clear up it does become cracked and can bleed because the medicine that clears it up often gets on the skin surrounding the wart. I found this out after using the liquid remover and so with my daughter's second wart I got the little medicated disks. They are little round dots that come with a little round bandaid to put over them, they hurt less than the liquid remover, are easier to apply, make it less likely that cracking and bleeding occur, and seem work pretty fast.
You could try putting Neosporine on it until it heals and isn't bleeding anymore and then try the disks or if the area is really red and looks infected though I would take him to the doctor to make sure it isn't infected and to see if it is indeed a wart. Better to be safe than sorry.