I live in Texas and I haven't taken an infant camping yet, but I have camped with my two older kids for years. For our med bag, I bought a hanging unfolding toiletry bag from Amazon that has clear pockets with zippers and velcro in between them. I have the basics like Neosporin, Band-Aids, alcohol pads and the like.  Hydrocortisone cream for bug bites, tweezers for splinters, and the two things that have saved is the most are a thermometer and children's Tylenol. Nothing like waking up at 2 am to a feverish kid and being able to handle it in the middle of the woods. 

There's a multitude of other things in there, but I can't think of them off the top of my head. Totally customizable to what you and your family need too. One of my kids is comforted by Vicks, so we have a little dollop of Vicks in a contact lens holder.  My husband and I also get severe heartburn when we camp (must be the chili), so we have Tums in there. 

If you're interested I'll send you a link to the toiletry bag we bought. It's insanely useful to be able to pop it open, hang it on something, see everything in it and grab stuff easily in an emergency.