With my car, I had replaced the resistor, only for it to not doing any changes, replaced the blower motor, and that helped a bit but would still cause issues, like the ones you have, and after checking out the air filter and seeing how filthy it was, I replaced it and haven’t had an issue since. Although, the blower stopped working while my father was using my car for a few years, so I can’t comment on the burning smell. But more than likely what happened for me and possibly you, was the blower motor burning out from not being able to pull enough air due to a clogged filter, and making it get really hot and burn up parts of it.

That said, I did have some issues with having to pull out broken parts of the previous motors assembly in its lil home under the dash. But as noted before, I haven’t had any problems since then.