As it was written befor, 3 weeks isn't really long. Try again and again and keep doing sports.
Also it depends on the kind of push ups you are doing. There are hundreds of different kinds. If you are stuck at one, perhaps try switching to another kind. Wide arm, close arm, diamond, elevated...
Also, look at your form. Is your back straight, your belly tucked in, are your arms like they should be for this kind of push ups?
When I restarted doing sports some times ago I could do 20-30 push ups. But I tried e.g. Convict conditioning where you start doing push ups against a wall. It seems easy and silly, but if you do in slowly and if you concentrate at that time on all your movements you will greatly increase your skills. then I moved after one or two month against a wall to doing push ups against a table. Still easy enough to concentrate on your form and so on.
There a plenty different body weight books and programs out there. Convict conditioning is just one of them I tried and had fun doing it. Have a look what suits you best.
tl;dr: look at your form, try different styles but keep doing push ups :)