Will 250cc and 275cc Breast Implants Give Me Mid C Cup?

It is impossible to give you an accurate answer without a personal consultation.  You should go back to your surgeon and try on different sizes.  Bring in a bra you wish to fit into and see which implants will get you there. 

This is a tough question to decide by the information given. The reality is that you'll need to visit with your ABPS board certified plastic surgeon and then decide what size to go with. Some of us use sizers in the office using a bra under a form fitting shirt that you can then see what size you are headed for.
The other's have mentioned the importance of measuring your body frame dimensions. I use those measurements as well to help guide our choice. The reality is that these implant companies use these measurements as a bit of a marketing ploy to get you to feel like you have the exact implant that was designed to fit your body. It's not really like that. In fact, the two implants you have selected thusfar are probably not the ones that I, or some others on this response list would've recommended. That doesn't mean you have the wrong ones, it just means that there's several that you would look great with.
Fortunately, by your dimensions you sound like an excellent candidate. All you need to do is have a better idea of what size you'll end up being. The A,B,C,D cup system is a ballpark that we use to communicate with patients but if you get the exact same bra back and cup size in a few different brands, you'll see what I mean. Don't rely so much on the cup size but try some implants on and see what look you're going for.
It sounds like you're in the right vicinity since you're a tiny frame. You'll hear from other girls that they went larger and barely got into a C cup. Don't let that confuse you. Those others may have totally different body frames and smaller breasts to begin with.

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 in a thorough implant sizing session.Implant sizing depends on several factors. One of the most important factors is your breast width. Generally, your surgeon will measure your breast width, and then provide you with a range of implant sizes appropriate for your native breast size. There are more nuances to it than just what I've described, but this approach works for most women.I usually have my patients bring in a large bra and a tight t-shirt to do sizing. I'll then choose 3-4 implants that I feel are appropriate, and have my patients place them in the bra under the tight t-shirt. My patients can then look in the mirror and get a good sense of what they will look like with the provided implant sizes. My patients like this approach and get a great idea of how they will look.By using this technique, your surgeon can outline a range of appropriate implant sizes that will be aesthetically pleasing, and you make the final decision.I hope this helps. Good luck!Sincerely,