I just want to know if my transmission is going to be okay.

What is your question?

I just want to start out that I drove a stick shift for a while and it took me a bit when I got a new (used) car to get use to not shifting and a clutch not being there. With that being said, today coming home from work I was listening to a song on the radio I use to play in my old car. I was going down hill and for whatever reason I just felt the need to put it in neutral. After realizing what I did I went to put it back in gear but shifted up instead of down. (As if I was going back in gear) and accidentally put it in reverse with out hitting the break going down hill. Right after the transmission jumped as quick as I could I put it back in drive. My car doesn’t seem different. I stopped it’s shifting fine and not making any sounds out of the ordinary. I just want to know if I could have done serious damage and if I should get it check out? I’m not a mechanic and don’t want to ruin a car I just got.