First of all, well done for being brave enough to seek out help on a difficult situation. 15 is not an easy age to cope with.
Right now the rejection you feel might hurt a lot but I promise you that in a few years time you will think back to now and laugh. Your young mind is having to take on the onslaught of the feelings of adulthood for the first time.
Secondly, don't take this girl's rejection personally. She is rejecting your age, not you.
To put things in perspective, she is 19 and you are 15. The equivalent circumstances would be an 8 year old girl getting the hots for you and asking you out. Not such an attractive thought is it...
The reason you would not be interested in an 8 year old would be due to her age, and nothing to do with her as a person.
It is the same for the girl you are interested in. 19 is a world apart from your age, and as has been mentioned, girls that age will be looking for men a few years older than she is, because girls mature quicker than boys.
Lastly, the best advice to get over your feelings for this girl is time. I'm sure she will continue to melt your heart every time you see her, but facing those feelings and learning to cope with them is going to help you deal with the next stages in your life. Now is a great time to start learning these coping skills.
What might help is looking for girls your own age. Just don't be in a rush. You have so much to learn about yourself right now, and you are still changing. The kind of girls you like at your age now might not be the kind of girls you will like in the future.
Feelings are tough to deal with. It's going to get harder too. Use this opportunity now to grow. You won't regret it.