Can I request a c-section instead of an induction?

I'm 37 weeks 3 days. My doctor told me she will be scheduling an induction for when I'm 39 weeks due to having gestational diabetes. Idk why, but the thought of being induced really scares. My biggest fear is the baby getting stuck due to me not being big enough (my sister had to have an emergency c-section because of this). Im also scared of getting induced and ending up needing a c-section anyway. A friend of mine was induced at 40 weeks and she was in labor for 12+ hours and only dilated 2 cm so she ended up having to have a c-section. I've also been told by multiple women that induced labor is much more painful than going into labor naturally. Anyways, this is my first baby and the overall thought of delivering a baby is terrifying me. I plan to discuss my concerns with my doctor at my next appointment in 6 days. Just wondering if it's normal for doctors to give you a choice..