Thank you all, for your kind help!
Yes, it was all about my bad technique; Too strong a grip directed all the vibrations from the drums, through the sticks absorbing into my hands.
Watching a bunch of videos on youtube, really helped me. Great advice!
I'm now forcing myself to use a much lighter grip, using mostly the thumbs and index fingers.
With some practice, forcing it wont be necessary, I'm sure.
Regarding digitaldarth's suggestion about a video of me playing?
No, no, no. I dont want to be the Worst Noobish Drummer of the Month or something, on the internet.
Thanks all. This really helped me!