Having had various 'first aid' kits, of many sizes, for years, I finally got to do a 'real world test'. I ended up with several rather bad infected skin sores on my right leg. Being into the 'prepper' lifestyle, I decided to 'self doctor' as if TSHTF and no doctor (and no modern meds) was available. I kept a close eye on things in case I did have to go in.....
So, basically I used Povidone Iodine for wound cleaning and germ killing, a few different brands of Antibacterial ointments - Neosporin, Polysporin and the generic Publix store brand. Pain came and went, no sign of going 'septic', but some major clear liquid drainage and the scabbing would get soft at times.
I'd wash it good with hot soapy water when bathing, dry it well, then treat with Povidone and the ointment, then wrap with three 4X4 gauze pads taped end to end (the wounds covered a fair sized area), and tape around the leg top & bottom. Eventually the drainage stopped, and real healing began. The scabbing would peal in places, especially after a good washing. Now, all scabs are gone, and it's healed.
I went through a good many (used three 25-pack boxes) tripled 4X4's, three rolls of one inch cloth white medical tape and half an 8 0z. bottle of Povidone (used liberally, but never on deep penetrating wounds!) and two small tubes of ointment. Wiped out the stock I had in my big Medical Box (large red plastic toolbox) - so I learned I need to store a LOT more of these items! As the wounds got smaller, I used some extra-large 3X4 inch bandades - but these never seem to stick well, and fall off too easily. Best to tape them.
So, you can bet I am repacking my smaller camping/motorcycling FA pouches. This was wih a fairly non-mobility threatening skin injury, NOT a deeper wound that would entail bloodloss and much more pain.
Any "First Aid Kit" is a compromise on what you can carry, and what you expect to encounter. We can't prepare or carry enough for EVERY possible injury, but I did learn some useful info.
I also pack a small snakebite kit (this IS wild Florida after all!) and a dental emergency kit.
A small flashlight or head light can be invaluable, and some saline solution if you have the carry capacity. Tent poles can double as splints.
In a pinch, any clean fabric and some Duck Tape can make a 'field expedient bandage' - been there, done that!