Regarding your concern that you might not be able to do 100 pushups tomorrow because you feel that it was hard to accomplish 100 pushups today. ... Maybe you should try to do 5 sets of pushups rather than 3 - especially if you believe that it is feeling so difficult for you?  There still can be plenty of time 1 hour to 5 hours between sets, of course having 2-3 hours between sets is good too. .but 5 sets gives you quite a bit of flexibility to make sure that you get in at least 100 pushups each day, even you believe that 100 might be a good and consistent goal that you might be able to reach and sustain (until all of your parts (including your wrists , or hands or whatever) become stronger). 

I still have shoulder pains, but my quantity of pushups per day and per set is continuing to mostly go up quite a bit, too.. so I don't really consider it to be overly problematic in that I consider that I am probably still growing and getting used to the quantity and the ongoing efforts to accomplish the amount that I am doing