From just feeling it, yes, it is common to confuse a fibroadenoma with a cyst. A sonogram should tell the difference thouch. A cyst is fluid filled and a fibroadenoma is solid, so they will look different on the ultrasound. In my case, the sonogram was diagnostic and could easily tell it was cancer. A fine needle aspiration is the first place to start. if it is fluid, it will collapse and perhaps never come back. My thought is to follow through with this doc, and then determine if you need a second opinion.
The lump needs to be looked at, no matter if solid or fluid. It may need to come out, but if the ultrasound showed it was a cyst, then a needle may be the best place to start.
80% of breast lumps are benign, and maybe even more so at your age. But you are smart to check it out, no matter what, and don't let them tell you you are too young.