without seeing you do a press up, its hard to tell whether its bad technique or not. how far apart are your arms, are you looking up or down, are you doing them on your knees. How often do you try to do them?
If you cannot do a full pressup, the only way to progress is to build up to it, although it can seem hard to break down what is seen as an already basic exercise. You could try using small hand weights in a chest press motion, or do press ups on your knees (with a mat of course), or leaning on a bench or table at 45 degrees to take some weight off your arms.
Then the usual rules of progression apply, try 3 times a week building up to an extra one every other session.
And remember, a little bit of wrist control always helps!