Starting in July of this year, at first I could only do two pull‑ups (if I didn’t lower completely, stopping at an elbow angle of 90^\circ I could do several). In September, because I couldn’t find a place to pull, I neglected it for a month.
Since early October, I’ve been consistent for a month; each time I lower fully until my chin is above the bar, I can only do four, pulling every other day.
At first you can try an elastic band or an equivalent. Essentially it makes each pull‑up a little easier; pure pulling might still let you do half a rep at the end, but fundamentally you can’t go further.
I should probably give up the resistance band; it’s meant for someone who can’t even pull it up.
During my sophomore year I used it every day, and I kept getting stronger, scoring over 20 on the fitness test, until I hurriedly vaulted over the dormitory gate and injured my rotator cuff.
Now my body can’t keep up, probably it’s already set and won’t grow any further.
Nevertheless, exercising is still great; it gives a sense of confidence.
Looks like you’re focusing on repetitions or on strength. These two are completely different directions, like Java and JavaScript.
Training for repetitions means using your body’s power to swing—learn it online, for example the butterfly pull‑up in CrossFit; many people who can’t do a single standard pull‑up can swing more than twenty.
Training for strength requires high frequency, moderate sets, low reps, and added weight—e.g., doing 5 sets a day, 3–5 reps per set; once you meet the standard, add a backpack for extra weight. I don’t specifically train pull‑ups; after each workout I just do a set casually, and at most I can do over 20 slow reps.
Pull‑up 15 reps:
https://www.bilibili.com/video/BV15b4y1V7QT/?spm_id_from=333.999.0.0
The senior practiced so well 
You can practice weightlifting, and even a casual lift will greatly help with pull-ups.
Weightlifting provides no help for pull-ups.