I've had moments where it's a little more sensitive than usual. It could just be sensitive from your uterus stretching out and pushing your organs around.
I would add that if you're at all worried about this, you should call your doctor.
ETA: With my first pregnancy I called my doctor about a lot of things that I didn't realize were totally normal but didn't realize I needed to call when I really did need to. Your doctor is used to FTMs and there is no concern that is not worth calling for.
There are definitely tender spots. Yesterday during the ultrasound there were times where I was like "ow can you move from there??" Or if my dogs step on my belly it hurts!!
My belly button is also extremely sensitive. And it popped out. I put a bandaid on it to try to smooth it a bit-won't do that again! It was painful taking it back off!
Re: Stomach sensitive to touch?