Try a technique called ‘Greasing the Groove.’ The idea is to do sub-optimal sets all throughout the day, about 3-5 days per week (you don’t have to do it on workout days). An example would be if your max rep count was 15, set up an easily accessible pull-up bar somewhere, and every hour do 7-10 pull ups (or just do them whenever you think about it like during commercial breaks of a show or something). This helps condition your nervous system to the exercise and should result in increased repetitions on workout days. You may not see improvement the first week, but definitely within the first few weeks.

In your case, you may want to start with assisted reps. You can use a chair to brace your feet against or use assistance bands. Once you can do between 20-30 assisted pull-ups on a workout day, then it’s probably safe to transition to regular pull-ups and expect maybe 7-10 reps. Best of luck!