I don't understand your objection to the piano. What are you considering 'classical' music. A lot of Mozart's, and other Classical composers work was written specifically for the piano. The list of available piano conciertos would fill several volumes of large books.
13 is not too old to learn the piano. Learning any instrument only takes 3 things:
1. Talent (about 20%)
2. Dedication, or heart, if you will... (30 %)
3. Practice, practice, practice, practice (50+%)
I am a full-time pro musician with 30+ years experience, and I play 10 instruments. I know what I am takling about. If you quit piano now, you will regret it later. After you learn, you don't have to play it as your main instrument, but knowledge of piano is indispensable for any musician or singer, regardless of what your favorite instrument is. Especially with the great MIDI technology available with modern keyboards (I make my own backing tracks this way) today, you don't want to bypass this invaluable tool.
Stick it out with the piano, for a while at least. You don't have to be a virtuoso on it. Just learn how to use it. You'll be glad you did.
Good Luck