I used topical antibiotics during my pregnancy, could my newborn have developed a tolerance to these antibiotics?

No. It does not work that way. The organisms that develop a tolerance to antibiotics are the bacteria they are aimed at treating. Overuse of antibiotics has caused an emerging problem of resistant bacteria that are very difficult to treat. Only use antibiotics if you absolutely need them. Don't use antibiotics for things like the common cold and other viral infections.
No. Unlikely that would happen. However using antibiotics chronically can lead to drug resistant strains of bacteria which is becoming a growing problem world wide.