would MEPS take a while to get back to me after i resubmitted my medical paperwork?

Lost paperwork doesn't move you to the front of the cue. There is a prior post where someone gave an excellent breakdown of the time period. Six weeks from receipt of the documents doesn't sound unusual. Don't be surprised if there is a request for additional documentation.
It is very rarely "sarge," and then only when you've developed a very strong relationship with that NCO, but mainly it's only in movies.
Drill Sergeants really like being called "sarge." Especially when you say "Hey, sarge," or "Look, sarge," though (that was sarcasm).

You're going to have to wait. TBH, you're a number until you hit E5, and since you're just a civilian, don't expect to be pushed to the front of the line for anyone's convenience other than the army's. It sucks but such is life. I went through the same thing.

It took me 10 months to join the army due to medical waivers and the like (prior surgery) my packet ended up in Fort Knox being reviewed. This kind of thing takes time. Keep at it, paperwork sucks but it's what keeps the army moving.

Second... Point of clarity. It's spelled "Sergeant" not "Sargant" and when shortening the word, the most you'll hear is "sarn't" and even then some NCOs are particular about it. No one says "Sarge" this isn't a WWII Hollywood movie.

Also, since you're going into the army, I'm gonna give you a little hip-pocket training while I've got your attention.

In the army, don't excuse yourself for asking a question. Don't offer an explanation as to why you're asking the question. It's implied that you want further information since you're asking the question. If you do that at basic training you're going to get chewed out for wasting more time in conversation. The army is all about bottom line up front (getting out the question or info you need to convey with no fluff). Ask your question and get your answer. Only offer the "why" if you're asked for it.

On a similar note, if you mess up, don't offer excuses and try to explain yourself. The army is all about business, it's not personal. (even if it is) just keep your mouth shut and answer the questions asked of you.

I know I may sound blunt, but it's just the army way of doing things, especially during initial entry training.

Best of luck, I hope it all clears up soon!

That happened to me too. I had to submit paperwork for two screws in my ankle and MEPS lost my paperwork. I resubmitted it and it only took a week to get back to me after that. Initially, I had waited a month and a half before I found out my paperwork had been lost. It probably will depend on the busyness of the MEPS, the time of year, the severity of your injury, and other factors. I don't think anyone can give you an exact answer because getting records like that approved is a case by case thing. They can't put you in front because you have a special case and have been waiting longer. There are probably several people with the same kind of records trying to get their records read. It sucks but you have to be patient.