I have small red dots that have appeared on my breasts over the last few days. is this something to worry about?

Unlikely: probably not anything lifetheatening, but it's always hard to render an opinion on a skin condition without looking at it. Could be folliculitis, or an allergic reaction to clothing or a bra, or a heat rash. If it doesn't go away on its own in a couple of days or gets worse or you develop fevers, chills or anything else concerning, you should have a doc take a look at it.