The pictures do not show up very clearly but it does not appear to be warts to me - and - you say 'these bumps' and I do not think several warts would appear at one time - but not sure about that.
Take a look at these images (pretty graphic) and see what we mean about what a wart looks like. There are quite a lot of different kinds of warts so try to look for a match.
I believe your son got into a bug nest of some kind; could be some kind of ants or even mosquitoes as several can bite in several places before they stop. You also say it is hard and has a point so that would indicate the poison under the skin and maybe part of the insect still there.
There are several things you can try to relive the pain and itch.
1. Use ice cubes or crushed ice or even a wet cloth (placed in freezer) on the spot or soak hand in cold water. You'll have to judge how to do this - according to your son's age.
2. Soak hand in white or apple cider vinegar.
3. Soak hand in warm/hot water that has a 1/2 or more cup of regular sale or Epsom Salt (better). Use as hot as your son can take but test it first. Dunk hand in and out a couple of times to adjust to the temperature of the water. This will draw out the poison and provide pain relief. You can do this several times a day. You can reuse the same water if water is clean - up to you.
4. Make a paste of baking soda and vinegar and place on spots. You may have to wrap the hand or use band-aids to keep paste in place for a few minutes.
Just putting Vaseline or ointment on the spot and covering with a band-aid will ease the pain until you can find a better solution..
Take you son to see a pharmacist and let him tell you what would be good to use - probably Cortisone Cream - they will know if this is a bite or something more serious.
I would have a health care professional check them out especially if they are painful and more than one. They don't look like warts but the photos are not the best on my screen. Warts are typically flat and you a describe a point. There's are many allergic reactions and eczema types that fit your description. Better safe than sorry! Prayers for healing.
These do not look like a wart but rather a bit from something. I would take him in and have them looked at to make sure.
It looks more like a bite. Ask your son if it's at all itchy or has been itchy, and if the pain is more of a headache type or a burning type.