Hey, it's absolutely normal, that playing a hand-drum maybe a little painful in the beginning (same with guitar too...). Think - it's causing enormal stress on your fingertips! So what to do....?!
You may strengthen your fingers some times a day even by the way. Look to this video:
Mainly you only need a surface to hit it with your fingers. It doesn't matter wether it's a table or a book wich you may carry with you. Do it with ease and don't worry about speed: The easier it goes you may increase speed with no problem. So, whenever you have a break, you may training your fingers for a few minutes. That's first.
Next, stop drumming immediatly, when it starts hurting. Take a rest instead. - There are two kinds of pain, you should know: First is lokated in soft parts of your body. This pain is ok. You need to come closer with, it's lowering by time. But be aware, if the joints in your hand are hurting, the tendons too - that may cause serious injuries! It needs to correct your position fundamentally this case!!!
So, hopefully I might help you a little. Please tell something about your progress.