My car makes a loud squealing noise when I start it and when I have my heat or air on. I also get a burning smell coming from my vents when I run my heat or air and I can smell it on the outside also.
Sounds like you might have an idler/tensioner pullie gone bad and belt is slipping on it. Normally not that hard a fix but according to the model some of the pullies are more expensive than others. Use caution driving it like this. If belt comes off you will be dead in the road.
Or it's the a/c compressor trying to lock up. It cycles with the heat on defrost. If it is the a/c you need to get it fixed.It will burn the belt off.
Have a mechanic check your belts right away- if you smell burning rubber, something in the belt department is ready to let go and leave you stranded