This is not the first time i'm doing a push-up but i think this is probably the first time i'm doing it well hence the pain on my right rib. I want to know if this is normal and if it is, should i continue my daily pushup or wait till the pain is gone.
A very common injury during bench presses or push-ups is a small cartilage or muscle tear in either the internal or external obliques - can also happen to the anterior muscle group, which are higher but usually this is not as painful. There are a lot of reasons why including not warming up, a previous injury, movement wasn't even (one side going up or down faster than the other), turning the trunk during the chest movement... There are generally small muscles and muscle/cartilage tears do not take much action.
These will feel like a "broken rib" or a stabbing pain the ribs. Do you need to see a dr for this sort of injury? If you want. Do you have to see a dr? No. There is no treatment other than ice and rest. When I was younger and muscles weren't as developed I had this happen several times. Usually a few days before the sharp pain goes away.