Just doing push ups won't work very well. They don't burn enough calories and only doing them could unbalance your body and cause you issues. To lose weight try eating a little less and moving a bit more. If there's no idfference after a couple of weeks, eat a little less still and move more. do whatever movements/exercise keeps you interested, cycling, walking, HIIT, lifting weights, just do it consistently.
use an online tdee calculator to get an idea of how much you should be eating each day.