Some reasons.
A thermometer should indicate a fever or low body temp and tell you if you have an infection or heat stroke or low energy, it can be a little subjective but still 103 on a cold day is a fever 101 on a hot day is defiately low energy.
Tubing is cheap lasts for decades and lets you feed little ones (aquarium tubing) drench adults and vent gas. Soft rubber tubing makes a good enema.
Funnels let you add the bloat aid or feed, so to the 60 or 20 cc syringes for smaller beasts
A range of syringe sizes saves loading syringes but the 6cc size is the most commonly used. If you have to subQ a dextrose injection the 60 is nice if you can handle it comfortably even if it needs several sites to inject it all.
The big 14 guage needle is for venting gas in a lamb only. I use an 18 for Vitamin AD which is oil based and thick, on ewes. I'll fight it through a 20 for lambs. 18's can be good for subQ injections too. The 20x1 is my most used needle.
Duct tape is a simple so much better at all weather holding tape than any medical tape I've used. Its great for making a "cast" for a broken leg too
Cotton is a simple absorbant wrap, KIS is my rule and it serves well. Also used for broken legs.
Heat bags (you could freeze them too) warm up lambs well. Any reheating of live animals takes care not to over heat the extremeties. I'll often use a warm enema too.
Mineral Oil use a universal lubricant for extractng dead lambs or a laxitive. lasts forever. I also keep Metamucil onhand as its a bit easier on lambs.
Oral electrolites are whjat most people use and they work fine. In smaller flocks you probably can note everyones condition better than me. I keep injectable electrolites to make up for lost time. Pepto has worked very well for my lambs and ewes that need it. A bit pricey but it earns its keep. Veg oil isn't a listed essential but it is a decent subsitute for bloat aid a bit of a laxitive.
Vit AD, sheep lose A fast under stress, and I use it on all new lambs. Sheep need D to absorb calcium for milk fever too. B Complex replaces lost thiamin somewhat, and stressed lambs especially need B to metabolize energy. E selenium in selenium poor areas is a given but ask your vet. They need E to absorb selenium. Thiamin is listed seperately and is used with Dexamethasone to treat polio of a thiamin deficency condition brought on by rapid feed changes of type or amount or just because your ruminant critter afflicted decided to have a problem. Thiamin is produced in the animal's rumin.
PenG is used for dirty wound infections, aspirated pnuemonia, foot rot, mastitis, rotten dead lambs after they are extracted......... and a host of others. Oxytetracycline is the first line fo defence against Pasteurella Pnuemonia, Pink eye, and a few others. There are stronger broad spectrum antibiotics. Trivetrin or Borgal and it goes by other names too is an injectable sulfa drug useful for some pnuemonias, foot rot, and other PEN G type infections. Sulfa methazine is an oral cocidiosis treatment, simple and fast acting.
Injectable Calcium is used to treat milk fever, or a calcium deficency. First time lambers and older ewes get this too commonly not to have fast access to it. You need a Vit AD shot too for the D to absorb the Cal. Cal Mag Phos is used to treat grass tetny although if you start sheep on fresh grass slowly you won't likely need it. Injectable dextrose is often 50% strength. I cut it with boiled water to 30%. 50% is too strong and will cause an inflamation and stinging/stress at the injection site. Full strength I use it to give struggling new borns a quick oral dose of energy.
Oxytocin is used to assist lambing if the ewe is fully dialated and is not pushing in a timely fasion. It is subjective and pulling the lamb is often a better option. Its also used in half doses for milk let down.
Tasvax8 or a similar 8 way cattle vaccine will likely save you sick/dead lambs and sheep. Its very cheap insurance.
ASA {asprin} lowers fevers, reduces pain just like in people. Get a vet to explain the dosages, as they are very much higher for sheep.
I forgot Iron injectable for anemic worm infestation survivors. helps rebuild the red blood supply. Optional.
The pad of paper and Pen acknowleges that we all forget things and a record saves trouble at every step. Trouble that could cost you more than a sick or dead sheep.
HTH