I am a 34b between 115lbs and 120lbs 5'6, is going to a D cup too big for my frame?

Without a physical examination or, at the very least, photos, it is difficult to respond to your question with accuracy. However, cup sizes in bras vary, and Victoria's Secret, for example, tends to upsize. But going up two cup sizes is possible with breast augmentation. To determine which breast implant size is best for you it is important to first find out what your specific wishes are not only with words or letters such as cup size or “not too big” or “natural”, but also with a visual understanding of what you hope to look like. This can be accomplished either with photographs of patients whose breasts and body type look like you, or ideally with photos of patients not only whose breasts and body type visually are similar to yours, but are also a similar height, weight, and pre-operative breast size. In our own practice we have provided that unique functionality on our website to accomplish exactly that. 
Unfortunately the most common reason for a woman to be unhappy after her augmentation is feeling as though she is either too big or not big enough. Thankfully, in our practice this is rarely a problem because implant size selection is what we spend most of our time discussing and determining. I do not place the onus of selecting the breast implant size on my patients since they are coming to me for my advice and expertise, but I do ask my patients to be as specific as possible about their aesthetic goals and I then advise them accordingly. 

I would advise you to seek the advice of a board certified plastic surgeon experienced in breast enhancement surgery and make sure that your own sense of aesthetics aligns with that of your plastic surgeon. Your idea of “natural” or “pretty” or “proportionate” might be different from your plastic surgeon’s and it is very important for you to feel confident that you are both of like minds as far as the goals. Best of luck to you and I hope you are successful in achieving the enhancement you are seeking.

Thank you for sharing your question and congratulations on your decision to pursue a breast augmentation.  Each patient has their own expectation on a goal outcome and for some a D cup may be too large while for others it is too small.  Remember that a bra size is not representative of a discreet appearance or size as differences in implant style and profile as well as the soft tissue of the patient will effect your result.  It sounds as if it may be useful to try on sizers in your surgeon's office to be able to find an implant that best meets your expectations.  Best wishes.