I'll be 35 weeks Friday, and I feel exactly the same. It wouldn't hurt to bring it up to your Dr, the worse they can do is say no. I hope it works out for you! @franchesca
You can. Most drs (at least where I'm living in Ohio) won't induce you before 39 weeks unless it's medically necessary. I asked my Dr about it and she said the hospital won't let her schedule anything before 39 weeks.