No, you won’t go to jail, so long as you keep it strictly platonic. I think it’s really cute. It’s probably not going to end well though, unfortunately for you guys. I think your mom is just trying to save you some heartache, in her own misguided way.
As you both get older, the relative appropriateness of your relationship to society changes. A three year difference is nothing if you’re both over 18. But an 18 year old dating a fifteen year old is on the very edge of acceptability, you better not be having sex and God help you if you get her pregnant. Ditto for a 17 year old dating a 14 year old.
My advice to you is to scale back the emotional intensity of your interaction. Don’t do it all at once, just realize that your relationship is a long shot and try not to invest too much into it. It’s the sort of thing that can really cause a scandal if not handled well. The last thing you want in your life is accusations that you raped a 15 year old.