Welcome to NeuroTalk:

First off, I'd recommend you suspend the weight lifting/pushups for a while. See if things improve.

Secondly, some people get compression paresthesias at night.
I believe the most common reason, is low blood sugars. Have a balanced snack before bedtime, that has protein in it, and not too much sugar or carbs. I use Zone bars, because they are balanced that way. If your symptoms abate with a snack then you can try to watch your diet, avoid too much sugar/carbs, and eat quality protein and good fats. This can balance your blood sugars so you won't get lows.

Sometimes strains, esp the tendons, compress nerves, so avoiding stresses on the wrists may help. Inflammation around the tendons can affect the nearby nerves. You can test to see if inflammation is your culprit by using some NSAID orally like Aleve and if it works then you know you have inflammation.

Salonpas patches on the wrist may help too. You can get these at RiteAid or Walgreen's, and some WalMarts. The original one is very inexpensive (the fancy new arthritis one is not necessary) and can help alot. Some people find an ice pack on the wrist helps too. Just don't do it for more than 20 minutes at a time.