Oh no >.<
If you're sure it's velvet then..
•Symptoms: Can be found by shining a flashlight on your betta. If it looks like it is covered in fine gold of rust colored dust then it has velvet. Clamped Fins, no appetite, darting/rubbing, loss of color, lethargic
•Treatment: It is very contagious so you should treat the entire tank. Treat as you would treat Ick. PP is also my favorite for treating Velvet."
(PP is Potassium Permanganate although I have no idea what this is!)
It's generally advised that you keep them in absolute darkness (covering the tank if you need to) while treating velvet.
Don't feel too terrible for transferring it from one fish to another. In all honestly, if any of my fish in either of the two tanks got sick I'd probably transfer it as well. I'm short on cash so I don't have a separate gravel vacuum or anything like that. So I definitely have cross contamination between both tanks.
The best you can do is learn from the little mistake and take care when treating. Best of luck and keep updating and posting if anything changes. Someone will definitely be able to assist you with this.