Do i need to go to the doctor if i was shaving my "down stairs" with a razor that had a little spot of rust ?

No: Touching rust if not a problem. People use, handle, and play with many metal objects or tools that have rust on them. The "stepping on a rusty nail" concern occurs because germs are pushed through the skin wound, deep enough to cause an infection. However, razors shave better if they are smooth and rust-free, so a rusty razor should be safely disposed of.

Rusty razor: Were you cut by the blade? How long ago was your last tetanus shot? If it has been ten or more years ago - would get another one.