I don't have a special diving kit; just a general one (actually, two) for outdoors. It works well either way. I organize the kit into 4 modules: orthopedics, wound care, general purpose, and meds. I have two kits. The "base camp" kit is comprehensive and often tailored to the outing; contains advanced gear, some special perishables/meds, and extra inventory of basic supplies. The "mobile" kit is just a very basic first responder kit to stablize someone enough to reach the base kit or evacuate to next level of care. Using it requires minimal training. It has almost no meds except for only the most comon type. No breakables. Everything is readily available from any pharmacy; some items such as the burn-gel packets and SAM(tm) splint are usually available at industrial supply shops which stock items for workplace first-aid kits. It all fits easily in a fairly small fishing tackle box or several small Rubbermaid-type containers.
Ortho....elastic compression bandages (I prefer self-sticking Coban(tm) (latex!) but also pack some traditional fabric Ace(tm) wraps), SAM(tm) splint; triangular bandage or bandana or large handkerchief, chemically activated cold-pack.
Wound.... exam gloves; I prefer nitrile over latex and vinyl and these can also serve as occlusive dressing or elastic bands when cut up. Sterile eye wash which can also serve as wound rinse...assorted gauze pads (mostly; general purpose 3"x3"), roll bandages; waterproof adhesive tape (2in wide size, tear into thinner strips if needed); small roll of duct tape (the glue is fierce but better than most adhesive tapes; avoid encircling limbs with non-elastic tape), liquid bandage (small, clean, superficial cuts only, no active bleeding or exudates, can sting like fury but flexible and occlusive), assorted band-aids (Band-Aid Sport Strips(tm) are flexible and tenacious), tincture of benzoin (optional stinky, staining stuff but greatly increases adhesive holding power, use only on unbroken skin, some people may be allergic), moleskin/molefoam, hydrogel pad (e.g. Spenco 2nd-Skin (tm)),
General.... CPR mask (but remember that chest compressions are the priority), fine-pointed tweezers, penlight (I use a small bombproof 2-AAA UK LED keychain light), mirror (a metal disc platter from a dissected PC harddrive works great), assorted plastic zip-loc bags, a couple of large garbage bags, some aluminum foil and plastic wrap, cotton-tip swabs, EMT shears, magnifying glass, tongue depressors, mylar rescue blanket, safety pins, a bit of telephone wire, butane lighter, spoon, disposable single-edge razor blades, grease pencil & slate.
Meds....aspirin, ibuprofen, antihistamine, decongestant, sunscreen, burn gel packets (e.g. Water-Jel(tm); 2% lidocaine), topical antiseptic wash (Hibiclens(tm)), packets of alcohol swaps, packets of hydrocortisone.
This was all from memory and so I might've left out a thing or two. But I hope it's helpful. Maybe local knowledge will suggest including other items.
Whatever gets into your kit is based on:
1. ETA to next level of care
2. Most importantly -- extemely importantly -- know how to use everything in your kit, especially any meds. If you're not sure, ask someone who's qualified and/or get trained. Remember: Do no harm.... Good samaritan laws are not usually unlimited...