Re: Something wrong with my sax or something I am doing??
Since the problem comes and goes, it sounds like either a sticky key or a change of reeds. Breaking in a new reed, especially if you're playing with a hard reed, takes a lot of wind to make the horn perform. As the reed gets broken in, it's easier to blow.
Squeaking on the middle register G or above sounds like you have a leak somewhere. You should take the horn to a really good repair shop to get this fixed.
So - possible key sticking and possible leaky pad. Maybe you need a repading job. Those aren't cheap but that sounds like what's needed.
Now - you mention a student rental - why not take the horn back and get the rental shop to swap it for another horn? That's bound to be quicker and less expensive than fixing the horn.
Good luck with whatever you decide to do.