Hi Cindy,
I had problems with my wrist at the beginning of my practice and it developed into a proper tendinitis. I learned a couple of things during those months. First of all, the hand is not a foot. The hand cannot take all the weight in the “heel”. One really needs to push into the mat with the tips of the fingers and the part between thumb and pointer. You should almost feel the heel of that hand hovering over the floor instead of sinking deep into the mat. In the same time, the fingers are widely spread. I usually do not spread the thumb as far out as I can, but use a comfortable wide angle.
To strengthen my wrists and avoid re-injury I often do little hand exercises which I find in the internet (hand yoga or so) and tendinitis rehab exercises. Maybe they can help you, too?
To be honest, it does not sound right, that you can touch the ground with your heels in down dog. Do you have very flexible hamstrings? Many beginners including me got into class, thinking to be a lot more advanced, just to end up being corrected: “Bend your legs, bend your legs more!” When you see a good down dog, the line from the wrists to the bum is absolutely straight. Some can even get it concave. Try to bend your legs a bit and then push your bum up in the air as far as you can. Does it feel different? From here you can carefully straighten your legs and lower the heels without moving your back at all.