Don't ignore it as it can get worse. Use bands that are not so strong as much as possible. Shoot less at one shooting session. Learn to shoot without holding very long for sighting. Shoot every other day, or even one on and two off to allow more time for muscles to repair and build up. Hope that helps!! All the best!!!
You could use a wrist brace or add a hole into the slingshot for your little finger to fit into that takes away any pull from the forks if you are using strong bands, or just downsize and use weaker bands and smaller shot until it's better.
I hold it very tightly, I think pain is due to that...., I use only 2 slingshots, Chinese one - Similar to General Hunter with 1745 tubes & Perry's PS1 with double bands (gum rubber). largest ammo 12mm, but most of the shots from clay ammo..
I work in a Physical therapy office. Best thing is to ice it and rest it. if you do want to continue to shoot. Just use a simple ace wrap or you can purchase a wrist brace that does not hinder your moblity. they make many types, the one you want to look for is one utilized for carpal tunnel or tendonitis. Also take over the counter Ibuprofen is you can tolerate it. After each activity you must ice it and rest it. If this does not work they make a specialty brace used for carpal tunnel that is worn and night to put the wrist in a non dependent postion to relieve the pressure on the nerves in the wrist. If this fails see an MD. Hope this helps.