I had same problem with pulling excercises. What I learned was that progression on pull ups is slow, so you have to be patient. You may focus more on pull ups, so you can train them often if you dont have soreness. When I was able to do only 3 chin ups(Im focusing on chin ups first because they are easier than pull ups, but you dont have to) max I did 20-25 of them in multiple sets, even 10 or more. If you can do 3 reps max, try after third one another pull up, even if you do half or quarter of pull up, it may help you with endurance. Instead of 3 version of pullups try to focus on basic pull ups first. Also you can try horizontal pullups (australian pullups/horizontal rows) or pull ups with some asistance (rubber bands or someone help a bit to push you over the bar)
I hope some of these tips help you, it worked for me.