There only thing to be aware of with skipping, is that you need to be landing on the balls of your feet, not the Heels, too much, or you might cause yourself Shin splints.
The other
slight possibility is you could have Tarsal Tunnel Syndrome, which is very similar to Carpal Tunnel Syndrome.
Tarsal Tunnel affects something called the Tibial Nerve, that runs down the inner side of the ankles, and underneath a Fibrous mass called the Tarsal Tunnel, there's also some Connective Tissues running through there too.
The problem can result from exercising or using the area quite a lot, and pretty much causes pressure on the Nerve itself. It can be relieved with NSAIDS, (Non-steroidal Anti-inflammatory things), possibly an Ankle Brace, Cortisone Shots, RICEing, (Rest Ice Elevation Compresson), or in the last resort, something called a Tarsal Release, where the Fiberous Tarsal Tunnel is cut, and relieves the pressure on the Nerve, and then it should heal back with scar tissue.
You could be assesed for Tarsal Tunnel, with something called an NCV, (Nerve Conduction Velocity Test), where an Electrode stimulates a Nerve to fire a signal, and another Electrode measures it.
The likelihood of you having T T in both Ankles, is highly unlikely, as T T is not that common to start with, but I couldn't say 100%, it's not possible to have T T in both Ankles.
However in this instance, I would still veer towards a Shin Splints scenario, as you may well have been skipping, and forcing the Heels onto the floor, as well as the balls of the Feet, and caused repeated jarring of Shins.
I would therefore utilise a Rice Method.
Rest.
Ice, which means icing the Areas, for 10-15 minutes about 3 times a day.
Compression, you could use a cold cloth for this, but it might be hard, as you might have to compress both at once, or one alternately after the other, so you might find it difficult to do this, and perhaps may want to omit this from your recovery regimen.
Elevation, keep the Shins off the floor as much as possible to avoid stressing them.
For future referance though, when you're skipping use the balls of your feet, don't bring the Heels down onto the floor, and you should be alright. I don't think this is in any way connected to the Osgood Schlatters you've had, as in possible Flexon issues with the Knee affecting technique, it's simply you probably landing on the ground with the full of the foot.
P.S. great thing for you to join a Kickboxing Club. I hope when you're feeling more recovered, you keep doing it, I think more females should do that kind of thing, and then some of them might not be the victims of things like muggings, or physical and sexual assaults.
You should be proud of wanting to do that as well as your weights and other stuff, so hopefully you'll be back on it again, soon, and I wish you a speedy recovery and best wishes with everything.
You should be very proud of yourself. There's a lot of people your age not into the things you're doing, and you'll be physically better off in the future for it.
GOOD JOB

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