A little bit ago I mentioned that you can improve your push ups by doing different variations of push ups.
Below is a quick workout that will help be able to do more push ups; HOWEVER, you need to focus on form and not just busting out as many reps as you can.
That may mean you have to really regress your push ups to continue moving with good form, especially as you get further into the workout.
You want QUALITY reps.
This workout will also help you balance out all of the pushing with some exercises to improve posture and activate your back muscles (which in turn, will actually help you with your pull ups as well!).
And in case you need a review of the basic push up and some regressions and progressions, check out this Push Up Form Post.
Make sure to record all of your numbers from the workout. While testing can be a great way to see progress, so can recording your numbers from your workouts.
If you do more push ups or a harder variation of push ups next time, you know your workouts are working!