I had the same problem when I re-started Yoga a few months ago. My instructor explained that the most likely reason was that I wasn't positioned properly - especially in Downward Dog, you really really need to have the WHOLE HAND absorb the weight of the rest of your body. In practical terms, that means sort of pushing your thumb and index finger into the mat -- the tendency is to place all the stress on our wrist & back of the hand.
I'd also recommend you do get at least a few sessions with an instructor - that's really important when starting Yoga. It's cool to do it at home and by yourself, but you might end up learning some positions wrong (very difficult to correct later because you get used to doing it the wrong way), and that can lead to the execises not being as good for you as they should, or even injury...
Oh, and make sure you have a good mat, and spend at least 10 minutes just laying down and relaxing at the end of the session.
Good luck!