You definitely need to do some research.
Induction based on size estimates is contraindicated and advised against by ACOG. First because growth U/S are off by +/- 2lbs, second, barring any medical complications it's very unusual that your body will grow a baby too big to deliver. Your size has nothing to do with the baby you can safely birth. Additionally, I'd be very careful with buying into what your doctor is saying about your pelvis being too small. Is there a real reason they believe this? Because it's hard to tell (unless it's some sort of actual malformation) and just because you are experiencing a lot of pelvic pain that doesn't mean your pelvis is small. I had SPD last time, it's just something that can happen for a variety of reasons.
Also, if you are concerned about baby coming out safely the number one thing I would tell you to do is not push on your back. That's pretty much the worst position to push in. Other positions will help you open your pelvis further for baby's descent.
Just based on what you've said here I would absolutely not induce. I'd actually be kind of nervous about what my OB was feeding me if I were you, TBH. Perspective is very important and going into labor with the mindset that baby might be too big isn't helpful for anyone. I was recently reading a study that was done that compared moms who had had late term growth U/S with those who didn't and even though their babies all ended up around the same size, the group who had had the U/S done had a much higher rate of C/S theoretically because the providers were less patient and the mom's were worried going into it (again, mindset is so important).
Just proceed carefully and definitely do some research! I know it's hard navigating the waters. GL!