My belly button did the same thing, it was very sensitive to the touch, and when I got to be about 30-32 weeks along, I noticed what it was. My skin was stretched to the max and especially having had my belly button pierced and removed the jewelry around 28 weeks, my skin was sensitive, and being stretched so much, I actually got a very tiny stretch mark right on top where my piercing site was. It looks silly, lol. But being that it was so stretched tight, it was sensitive and hurt, then a stretch mark appeared. It's possible that this could be what you're starting to get also, it's just in the hurting/sensitive stage. I don't believe it's anything serious if not though.
Im not sure. This is my second and ive never had anything like that either time. Maybe call your doctors office and see if there's a nurse you could speak with and just ask. Better to be safe.