Long a go in a place far away I was an EMT, and a soldier, and a forest fire fighter...
Any way, to day I carry a pretty extensive first aid kit, it is horse eccentric but it's also cheap and effective. It's in a 6 pack size soft sided cooler, with a hard insert, red. The primary contents are cheap premie diapers (hoof bandages) cheep maxipads (excellent trama dressings), cotton bating (old towls or shipping boots for padding the wounded limb) vettrap (a coadhesive dressing like the stuff your mom used but cheaper and about 4" wide and 15' long, stored in a small plastic tackle box that holds 6 it's isles If it gets squished as it sticks to its self, kids and careless stockers can ruin it) 4x6 non stick gaus, provadine iodine, drinking water, salt and a spray bottle. ( mix at .5% each salt and iodine, use spray bottle on stream to irrigate wound) duck tape (secures hoof bandage as well as emugency founder package)
Now I keep some cloth finger bandages, superglue and coming soon, Celox if I get really stupid.
Now this works for me, it can patch up a horse or me untile I we can get to the vett (wish the state would let him treat me too)
As to the Celox, it is an artificial clotting agent made from shrimp and crab shells that will plugg up a leak fast, and the doctored don't have to scrape and wash it out like Kwikclot (it uses potters clay) stuff ain't cheap but it's standard issue on the battle field and for EMS thesis days. You can get it in little 2 gram nose blead packs that work well on small nail and hoof knife cuts.
Any way, just food for thaught on what you can put to gether to slow down the leak till you can get patched up, that is if mom isn't around to bail you out (like your mom, mine always asked the same question, "is it bleeding?" If it wasent "stop wining" if it was " wash it off and put a brandade on it" after a wile I just went in and cleaned it up and if a brandade wouldn't cover it I used a wash cloth and went to the vett, err doctor)