Since you caught the ick early on in your tank, higher temp and Aquarium salt should work for them.
But for the new ick carrier? don't think so. You have no way of knowing how long he/she has been ill.
It's best to remove it asap to prevent any further infections and to medicate the sick one.
It also helps to keep the lighting low or off for the first few days. It helps to keep the fish calmer.
I learned the hard way about QT. I added 3 New Neon Tetras from a usually very good FS and a few days later my entire tank had a bad case of ick. Then one by one over the next eight hours, they all died.
It was my first experience with ick. I'd had fish for almost 6 years, no problems. Then wham! All gone in a day. It was horrid, but I learned fast about ick and quarantine. I've had a couple small ick out breaks since then but now I know the signs. I look for them every day and when I've seen it, it's always been early and I haven't lost another fish to ick since.
Of course now I've had to learn about popeye, bloat, tail walking, and hole in the head. I lost one to bloat and 2 very young cichlids to tail walking. I didn't know what they were, now I do and my fish are safer for it.
I started reading more and joined up here on AA. And thanks to everyone here on AA, except for a killer Red Zebra Cichlid, I'm not loosing anymore fish.
I had to take Sonny back to the FS where they are trying to rehab him a little before re-homing.
Good luck to you. And QT is the best thing you can do for all your fish. Not just for new fish, but even if you need to separate a fish for any reason.
I now have a 10g QT and a 5g hosp. tank. They spend a lot of time empty but I always keep them running just in case, we never know. They take very little effort or space and are a blessing when you have need of them.