Big Breast Implants on a Narrow Chest?

From your description of yourself and the photo of what you would like to be, the recommendation from your plastic surgeon is about right.  If  you are contemplating going a little larger,something in the mid 300's  would give you a nice C cup, but I wouldn't go much larger.

You need a proper examination by a ABPS certified plastic surgeon. You need measurements and discussions of size. You will then likely be a candidate for high profile or full profile (smallest base width for the size) implants.

Thank you for your question.

Unfortunately, without your photos, it is difficult to give you good advice.

For patients planning on breast augmentation surgery...it is very important to communicate your size goals with your surgeon.  In my practice, the use of photographs of “goal” pictures (and breasts that are too big or too small) is very helpful. I have found that the use of words such as “natural” or “C cup” or "fake looking" or "top heavy" means different things to different people and therefore prove unhelpful.
Also, as you know, cup size varies depending on who makes the bra; therefore, discussing desired cup  size may also be inaccurate.  
I use  intraoperative sizers and place the patient in the upright position to evaluate breast size. Use of these sizers also allow me to select the breast implant profile (low, moderate, moderate plus, high-profile) that would most likely achieve the patient's goals. The patient's goal pictures are hanging on the wall, and allow for direct comparison.
I have found that this system is very helpful in improving the chances of achieving the patient's goals as consistently as possible.

Make sure you are seeing a surgeon with extensive experience who can show you results.

Best wishes.