That does not sound good frypup, I suggest you ditch the jelqing for a while.
But let me see, I read your op and you do your “wet ” jelqs, without lube. As memento suggested, it could all be down to the lack of lube and skin pain. You hold the skin at the base so it makes sense that if stretched you would be sore near the base, then your grip slides on the skin wthout lube so you get burning sensations and the skin is irritated.
Try a good amount of olive or coconut oil, shea butter is my favourite and it helps moisturise the skin well.
Also, stop holding the base when you do your jelqs and don’t do them flaccid it would be nonsense imo.