Of course it’s going to be loose before you get your boobs….Also I was a 34B before and can no longer wear bra’s with that back size; only 36HH, the 34 simply doesn’t fit anymore so you never know.
I would stick with the medium and buy a few 34 back sports bra’s too, especially as you are aiming for an E…It’s supposed to be tight but not so tight that is causes you major discomfort xx