Hello
I also use the gel and have dermatitis at the moment- little splits in skin so am trying v hard to apply carefully. However, I did get some in there a couple of times- the alcohol stung. No adverse reactions.
I'm sure you will be fine. Try and apply to another area eg upper inner thighs for a while until the insect bite heals. I'm not a doctor, of course, but having had trouble myself a couple of weeks ago trying to avoid using the sore bits of my hand, I've been fine. All healed now but I did think of using a plastic glove. But decided my hands washed would be more 'sterile?.
Am sure someone else in the know will be along soon but try not to worry.
You could always check with the doctor if you are concerned but I don't think they would be worried- probably say the same thing? Just avoid that area and use a different hand??
Xx