Is doing only push-ups and pull-ups harmful? Will muscles grow unproportionately? I'd like to build muscles but I can't get a gym membreship.
Depends on how you exercise and your body composition. You absolutely don't need to go to a gym to become muscular, but you do need proper nutrition, and you need to exercise properly. The number of reps you do is less important than your contraction and form, and giving yourself time to recover rather than working the same muscles daily is also better. If your a light person, doing body weight workouts is much less effective than a heavier person. And you need to have exercises where you can't exceed more than 10 reps if you want to add size to your muscles.
You suggested pull-ups and push-ups. Pull-ups are a very good upper body exercise, but don't do wide pull ups or bring your head in front of the bar, these exercises put stress on your shoulder ligaments and rotator cuffs which will lead to injury and damage. For pushups, I did a lot when I was in high school and stuff, but found them to be ineffective and stressful on your wrists. They are great if you can't do 10, but I switched to dips. After about a year of doing dips, my wrists and shoulders began to hurt and I stopped doing those as well. They were becoming useless anyway become I could do 20 at a time. For triceps, I now do body weight tricep extensions. You should look into them, it's much more effective and no stress on the wrists, and keep your elbows in to avoid shoulder stress. Squats are also useless over time and are stressful to your knees, this goes for running too. Plyometric lunges are good, just keep your weight evenly distributed to avoid stress on the knees. Jump squats can be very good for explosive leg strength as well as on legged calf rasies. And having strong legs make running feel weightless.
I would look into videos and more sources for a good list of exercises, but consider my warnings about pushups and such, many even experts will recommend exercises that really are not effective and can be stressful on joints and ligaments. I take pride on being a very strong and healthy athlete naturally without ever stepping a foot in a gym. Hope you feel the same someday.