I really want to join the Military in my country but a year ago i injured my right wrist and even though it has been healed and im able to fitness and such i with no pain i do continue to feel pain only when im doing push ups.
Is there still hope for me to become a soldier?

What does your doctor say?

Just so you know, the physical fitness tests required are X number of pullups, X number of situps, and the run in set timeframe and distance. Pushups are not part of the requirement. However, during boot camp they are used as a form of physical conditioning for the recruit.

If by "physical conditioning" you mean getting smoked, lol. Way to candy coat it all the way gunny.