Hard to answer your question without photos and measurements. That being said, I doubt that 350 cc's will take a small B to a D. Best to try on implants at your next consultation to get a better sense of size. Best of luck.
There is no way to guarantee a particular bra size. Bra sizing varies greatly between bra manufacturers and a C in one bra will be a D in another. What matters more than the assigned bra size is the way the implant looks on you. The best option for your body and aesthetic goals can be determined...
Your implants will drop faster but there's a risk of displacement. That's why I tell my patients to wear a bra, and just wear a bandeau to help dropping. But, listen to your surgeon because they know the details of your surgery.