375cc Too Big for a Petite Woman with Breast Tissue to Work With?

There are several other factors which will help determine this.I know this is a crude example but it helps to make the point. If you hide a golf ball (implant) under a silk sheet (tissue), the appearance will be very ball-like. However, if you hide the baseball under a thick comforter, the thickness of the comforter will greatly influence the result. A very thick comforter may make the ball barely visible. The comforter will determine the overall appearance of the result. If you change the golf ball to a volley ball, it may appear more round.

In individuals with very little tissue ( thin athletic women with low body fat and an A cup breast), the breast implants may be more noticeable and will ultimately have a significant role in determining the appearance of the outcome.

In individuals with C or D cup breasts, the overall breast tissue and position of the gland will have a greater effect on the overall appearance of the final result
 

To size you up for implants takes a physical exam and discussion of your goals. Everyone carries the volume a bit differently and the bras do not always correlate to the volume.
 

These do sound quite large for your frame especially if you are alrady a full B cup.  Make sure your doctor has specifically measured your width behind the breasts and that the chosen implant matches this width.  Make sure the profile of the impant matches the look and fullness in the upper pole you want.  And make sure that you know that at your height you will look much bigger, much quicker than if you were 5'11".