There is no problem halachically or otherwise with using tampons before you are married. In fact, it may be preferable for girls to use tampons to become better acquainted with their bodies. Using tampons can also alleviate some of the fears associated with doing bedikot and having marital relations.
The opening of the vagina is partially covered by a membrane known as the hymen. There is a hole in this membrane which allows for the exit of menstrual blood and which is generally large enough to accommodate a thin tampon. During first intercourse, this membrane is stretched to the sides and may tear slightly, leading to bleeding. Since women generally marry at a later age nowadays than they used to, and due to the use of tampons, often a woman's hymen is already stretched. There is no need to have this checked out. Halachically, you are considered a virgin as long as you have not had intercourse in the past. You will therefore be considered niddah after the first time you have relations with your husband, according to the laws of dam betulim.