2012 Volkswagen Passat - Burnt smell

I had the a/c repaired now I have a burnt wire smell out of the a/c vents when the air is on makes me sick?

There is a question whether or not it makes you sick? Take it back to the shop that fixed your AC and tell them what is going on.

Please tell us exactly which repairs were performed . . . you may have to refer to the invoice for this

No offense, but “had the a/c repaired” could mean lots of things, as there are many components in the system, and we don’t know if you had a wiring repair, ac compressor replaced, mode door actuator replaced, or what have you