It's very difficult to say, but your first priority for this goal must be weight loss. It's an excellent goal.

The answer is 'forever' at 220 lbs- apologies for the bluntness, but them's the facts.

That doesn't mean a pull-up can't be your ultimate goal, and keep doing what you're doing, but you've got a few things to do first- the first is losing at least a quarter, and probably a third of your bodyweight.

Being light makes pullups much, much easier. You're not going to outmuscle the equivalent of a 60lb weight vest on a 160lb girl, and 160 is still on the heavy side for females doing pullups. Can be done, if you're very strong, certainly.

All this to say, if you can't do a slow, controlled negative, it's a little early to start thinking about going up.

This is an excellent goal, to be clear. Just gotta prioritize your work.