The 25-year-old was forced to overcome a late reclassification that put her place at the Games in jeopardy, but still managed to finish third behind teammate Sophie Hahn and home favourite Veronica Hipolito.
Cox, who is also competing in cycling at the Rio Games, acknowledged that the change from T37 to T38 did make things more difficult, but stressed that being in the final alongside Hahn and fellow Brit Olivia Breen helped to get the best out of her.
"It's awesome. I came out here with the intention of getting a medal, but whether I was going to be able to do it with all the pressure, I wasn't sure. It was slipping away from me in that race but I managed to get back and grab that medal and yeah, it was an amazing feeling," she told Sports Mole.
"[The reclassification affected preparations] massively. Within the cycling it wasn't so bad because that was a bit early on and I'm quite far ahead in the world in that, but within the athletics it did kind of shove me a couple of places down in the world, so I did have to work really hard on the athletics side of things, try to put in the extra hours and stuff.
"I've got a great team behind me that have helped me massively. If it wasn't for them and the National Lottery funding, I wouldn't be in the position I'm in. It was really tough, mentally as well, having to dig in knowing that I'd gone from having a world record and [now] obviously having to work back. But I'm here - and I'm a medallist!
"I said if I'd got a medal it would just be perfect, just because I've worked so hard for it. This is the one that was going to be the toughest out of all of the events. It's awesome, and to have those girls out there with me is amazing. Sophie's a little pocket rocket and one day I'll reel her in, but for now it's great to see her achieve amazing things and to get her first Paralympic medal is a great thing to do."
Cox will be bidding to become the first Brit to win medals in two different sports at the Paralympics for 28 years in the velodrome on Saturday.