What do you do when your nails are disgusting and short they also have puffs at the top?

Generally, this is due to a nail biting habit. If you don't mind the aesthetics, don't do anything. If you do, consider nail biting cessation techniques. Either way, your nails will be permanently on the short side.

I have a girlfriend who is a major nailbiter. Her nails are about 5 mm long on average. I felt bad for her and let her start biting my nails, something she asked to do when her nails "ran out" of anything left to bite. She does it when we watch TV, in the movie theater, even while entertaining close friends (!).

Needless to say, after some years, my nails are about half their original length with a very similar "puff" on the finger tips that you've noticed in yours, presumably. They now look like the nails of a long term nail biter...even though I don't bite them that much (actually started after she began working on them. I couldn't stand their uneven tips and now I do it unconsciously at times).

But it did help her to grow her own nails, meaning the white part since her pink part became permanently shortened.

It worked but, truly, I don't think I would have let her start if I had to do it over again. I used to be able to pick things off the floor easily but not now.