The "excess" skin on the outside is the inner lips or Labia Minora. It is quite normal to have long inner lips after puberty.
You can have trouble with tampons for 3 reasons, 1) your hymen is partly covering the entrance, 2) the vagina is not large enough to get the tampon in and 3) you may not be wet enough to comfortably get the tampon in.
There was a time not to long ago when wearing tampons was not even recommended to girls of your age for these reasons.
You can try to use some of the applicator tampons with plastic applicators that are made for teens (they are smaller). Remember that if you are not flowing enough, the tampon will be difficult to remove, even though it may be easier to get in with a plastic applicator.
You can also try to lubricate the outside of the applicator slightly to make it easier to glide in. Also follow the instructions. It is important to stand in a position where the muscles around the vagina's entrance are relaxed and it is not shut. I am sure that because of your failed efforts up to now you are tensed up when you try. You will have to relax. If you have not yet taken a good look at what is going on 'down there', do so before trying to insert a tampon.
Lastly, billions of woman still rely on pads as the only means of protection. In some cultures the tampon is almost never used so don't let anybody put you off from wearing pads. Not all pads are the same so experiment with different makes and sizes to find the ones that are most comfortable for you.
