So sorry to hear you were bitten, Andre. You've not had many happy encounters with Range Rover drivers!
All best wishes to you for a swift and uneventful recovery. Keep an eye on how things are going Sometimes more problems show up in time so don't sign any waivers straight away. I was bitten in the heels by sheepdogs nearly 40 years ago and still show the effects, as the bites burst the capsules containing the fat in my heels and it herniates out when I am standing -- looks like ball bearings under the skin where each tooth entered.
As to your questions...
Should a cyclist carry a first kit?
It is a good idea, especially if one is far from people while riding, as I often am.
What should be in it?
Things! Useful things! I usually take a well equipped stock kit, then add the items I know I am most likely to need for a given situation. What differs is the extent of supplies. The one for day rides is smaller than the one for my extended expeditions. While on big tours, I sometimes take both the large and small kits. Because of its size, the larger one remains stowed in the bowels of my panniers, but the small one rides in my handlebar bag or rear jersey pocket where it can be readily accessed in an emergency -- when time really counts and one might not have both hands undamaged or available to use (i.e. the other hand is applying pressure to the wound).
If I am touring with someone (rare) I insist they have at least a mini-kit of their own. If they don't have one, I supply it for the duration of our trip together.
A key requirement for me is the kits *must* remain dry, as wet bandages and supplies are no longer sterile or even usable. For the mini-kits, this waterproofing can be as simple as a ziptop sandwich bag.
For day rides?
Yes, as mine can be 400km, so being as much as 200km from people means "far from help".
For extended tours?
Of course!
My kit contents are probably too detailed to include here in their entirety, but several ingredients I almost always add to my kits are...
1) A packet of clotting agent. These have expiry dates and are renewed about every 18 months. The granules can be poured into open wounds to stop bleeding (keeping a number of factors in mind...bleeding to a degree can cleanse a wound).
2) Beta-cyanoacrylate super glue, separate from the one in my underseat bag that is used to patch punctures in tubes and cuts in tires.
3) Sutures and thread. I managed to fall with my knee on the end of a diagonally cut sapling stump coming down a dew-wet grassy bridge elevation above the Rhine, resulting in a couple of deep cuts. After riding with it for another 60-odd kms, I decided it was time to deal with it properly when the adhesive plaster showed it was not up to the job. I stopped, cleaned things up and installed two stitches. After 10 days, I removed them and the wound was essentially healed. No further problems.
4) A pair or two of nitrile gloves.
5) Extra self-adhesive knee-sized large plasters...the kind with a non-stick face and peel off adhesive tabs I can apply myself. It is really hard to hold a wound shut and tape the plaster in place with just one hand.
6) My usual tube of neomycin-free antibiotic ointment.
7) I have weak ankles and flat feet, so am prone to ankle rollovers. For this reason, I add a roll of elastic bandage to my larger kit. It has come in handy for myriad other uses.
8 ) A good small knife with decent scissors for trimming plasters and tape to size. I prefer a Victorinox Classic or sometimes the serrated-jaw and liner-sprung scissors in Wenger's older offerings (Wenger was absorbed by Victorinox in recent years and many of their unique knife features were lost in the revamped offerings).
9) A small self-storing covered travel toothbrush for brushing out grit, sand, and gravel from the wound.
10) A small digital oral thermometer so I can tell "if I'm just hot" or genuinely feverish if/when a problem develops. Good early warning of illness or infection.
EDIT: Forgot to add (but should): It is a Real Good Idea to have training in first aid and wilderness medicine so you know how to use such items (I did and do keep up to date...it was an especially wise requirement in the days when I led bike tours professionally). Even a basic first aid course is really helpful.
EDIT 2: I tend to little wounds quickly (despite the knee story...it happened at a little after 05:00 and I needed to move on) before they can fester into something Bigger. It is amazing how quickly something small -- even a blackberry thorn tip -- can aspire to something More while on tour.
EDIT 3: If you are carrying other supplies, they can be pressed into service. In 1991 when my father was well into his 70s, we took a tour deep into wilderness where he took a bad fall going downhill at speed on crushed lava. The handlebar end took out two ribs in front and the saddle nose broke one behind. He was covered with road rash and the lava bits were deeply embedded throughout. After checking him for things like a burst spleen, we bound his ribs with spare tubes and he rode down another 1,100m in elevation to a remote fishing camp where I could clean his wounds properly. They had nothing on hand to clean his wounds, so I used the remainder of my dish soap, the rest of the alcohol from the stove, and the toothbrush I carried "just in case" something like that happened. It wasn't pleasant at the time, but he avoided infection and everything including the ribs healed fine. A number of mundane objects can be pressed into emergency service when needed.
All good healing wishes your way, Andre.
