Welcome to my wheelhouse: I work out regularly and know a lot of things about it.
Push-ups use your chest and triceps. Pull-ups use your back and biceps. If you do proper pull-ups, that is with your arms wider than shoulder width apart and your hands facing away from you, then you use more of your back than your arms, and because of your shoulder position you have less leverage, which makes them harder. If you do chin-ups, that is with your hands narrower than shoulder-width apart and facing you, you use more biceps than back, and have more leverage, making them easier.
If you go to a gym, there should be an assisted pull-up machine that lets you put your knees on a moving pad while doing the exercise. That will effectively reduce your weight, so you can do the pull-up motion with less weight than your bodyweight. You should also do lat pulldowns, which are basically the same motion except you're sitting down with your knees below a pad, pulling a bar down to you rather than yourself up to a bar.
Other exercises you can do to strengthen your back and make it easier to do a pull-up are single-arm rows, and pullovers. Single-arm rows involve a dumbbell and a bench: you put one knee on the bench, and the same arm as well, with your other leg out at an angle for balance, and you use your free arm to lift a dumbbell straight up and down to your chest; do it equally for both sides.
Pullovers involve lying on your back on a bench, holding a single dumbbell in both hands, but vertically; your palms should be flat on the inside of the weight load on one end of the dumbbell. Keeping your arms straight, rotate them back behind your head until the weight almost touches the ground, then, still keeping them straight, rotate them back up so your arms are vertical. Always be mindful of how much weight you're using, and if you ever feel sharp pain anywhere, stop immediately.
There are other back exercises, but they work different parts of the back than you use to do pull-ups. If you're taking working out seriously, you need to make sure that you don't overdevelop one set of muscles and ignore another, so you'll want to also work on your chest, shoulders, legs, arms, and core; the body is a unit, and you need to treat it as such.