Did I mess up my car battery trying to help jump another car? Jump start question.?

I made a total bone headed mistake. I've jump started several cars before just fine. I have a 2 year old Toyota Corolla. I offered to jump a Hyundai SUV on my break at work today. I know black is negative, red is positive.

I hooked up her dead car battery first. The terminal that was covered on hers was completely black so I thought it was the negative one. So I put the negative on that one and the positive on the other side which had no cover without thinking the positive terminal is always the one covered. Then I put it on my car on the correct terminals and sparks started mild as I was trying to connect them then got so hot and intense it partially melted the terminals on my jumper cables and sparks were shooting everywhere for like a solid 6 or 10 seconds. I disconnected fast because of the smell of burning and the melting jumper cables.

Upon rechecking, her positive terminal cover was black, but on the top you could barely see it had a red circle with a plus on it so I had it hooked up backwards on her dead battery and correctly on mine. I thought I was going to start a fire when I had done it. When I realized what I'd done wrong I switched the leads on her battery and I got her started and on her way.

My car was making a weird sound when the spark started flying, and the fact that the terminals started to melt off while sparking like crazy scared the hell out of me. I'm worried I could have done damage to her or my car.