A lot of doctors wont induce just because you are uncomfortable and also because even if baby is measuring full term the measurements can be off by lbs this late in pregnant. Most doctors will not induce unless you are 39 weeks. Ask the doctor to test you for cholestasis since if your levels come back elevated it puts baby at risk and they induce at about 37 weeks.
Talk to your Dr again. How many weeks are you? I was diagnosed with PUPPS (was questionable post-partum as to whether it may be cholestasis) and was induced 8 days before my EDD. My daughter was HUGE at birth, larger than full-term and I didn't get much sleep prior to being induced which made the birth more tiring!!!! Ask again, if you're at least 37 weeks it should be ok to induce. Good luck and I so feel with you :-)