In reply to Elsier:
My strength training is purely bodyweight (I tried lifting, it just doesn't interest me).
I think you need to be training 2-4 days a week. You need more volume than you are doing now to see improvements, but don't overdo it because overtraining is just as bad.
Start with regressions - knee push-ups and assisted/jump pull-ups. Do them until they are comfortable before moving on. When you decide to move on to the next progression, work on the negative movement (e.g., the let-down part of a pull-up) and get that smooth before adding the positive movement. Really really focus on form (this may cost you reps). If your form gets scrappy, either stop, or regress the movement to finish your set.
For push-ups in particular, if you are struggling, get someone to check your form. As someone else said, a couple of minor tweaks can really help (and can also prevent shoulder impingement problems).
Periodise your training. Don't just do the same routine every session. Plenty of advice on this online.
Have a long-term strength-related goal and work towards it. Mine are currently pistol squats and a solid free handstand (30 seconds free - used to have one of these, I want it back!). Working on the latter in particular gives me a little fun even at the end of a bad session.
Look at your flexibility/mobility. Poor mobility can make some bodyweight stuff a lot harder, particular if it your hips or shoulders that are tight. Also, you said lower-body stuff was ok for you, but if you have poor ankle mobility some squat-based movements can be harder.
Video yourself. Unless you are a narcissist, you will feel like an idiot doing it, but watching them back will highlight small improvements over time that you might not have noticed.
If you feel more comfortable reading or going to women's specific stuff that's fine, but don't feel like you have to restrict yourself to that - information targeted at men is just as relevant and there is more of it.
Have fun!
Post edited at 16:37