I've always had skin tags, but they have gotten really bad during pregnancy! (I have 25+ on my neck now and they seem to be popping up on my chest and under my breasts as well.) Fortunately for me, I do not have any on my nipple at this time. It sounds inconvenient. I know there are ways to get them removed professionally, but I will tell you what has worked for me in the past when I had one or two that really bothered me (these pregnancy ones are currently too small or out of the way to worry about or to do this with). If I was able to get a hold of one (tricky, I know), I would gently twist it. And twist and twist in the same direction. This seemed to cut off the blood supply from the base and within a day or two, they would dry up and fall off or I would be able to easily pull them off. I don't know how recommended this method is, but it worked for me on any skin tags big enough to twist and easy to reach. I have heard of people pulling them off themselves and that they bleed a lot.
I don't know anything about surgical removal but I have read things that give me hope that at least some of the pregnancy-induced ones will go away after pregnancy. Otherwise, I may have to look into it.
Now mom to DS1 born January 2010 and DS2 born December 2014!
12/08 (6 weeks),
1/13 (11 weeks), &
12/13 (9.5 weeks)