If you have a burning feeling at the tip of your penis and you were diagnosed with kidney stones, then this is an indication of a passing the stones. You should go for an MRI scan to confirm if it was a kidney stone.
I have heard coca cola can dissolve some types of kidney stones, maybe your stone did not pass through yet. But if the burning continues, you may have gotten a bacterial infection from passing the stone, it can happen. If this burning symptom gets worse or is not gone in a day or so, go to the doctor right away. Take care.