This one of those, "ON Scene" Calls that you have to make out in the field. If you have Arterial Blood gushing out, and the patient is likely to bleed out, if it isn't dealt with immediately, then yes, by all means, stop the Blood Flow, any way you can. HOWEVER, Should it just be a bad cut or tear, and not Arterial Blood, then depending on the injury, it may be wise to allow some blood flow, as this will tend to wash the wound, from the inside out, and take any pathogens with it. the Human Body can withstand losing Half the total Blood Volume, before serious issues, become irreversible. If IV Plasma Volume Replacement is available, and in use, then blood loses can even go deeper than that, and that is a LOT of Blood to splatter around. .... YMMV....
A few quick comments: 1. I prefer Bacitracin (triple antibiotic ointment) to neosporin. Many people get an inflammatory reaction to the neomycin in the neosporin. 2. For a contaminated wound, I recommend: flush wound with clean water, if possible, and let some blood seep out before dressing the wound (the solution to pollution is dilution). Start broad spectrum antibiotics immediately. You can get these for free from many pharmacies with a prescription. If you are packing the wound, first moisten the gauze with white vinegar (moist, not wet), creating an acetic acid wet-to-dry dressing. Change it twice/day. Most bacteria won't grow in an acidic environment. If the wound is wide, it can be loosely closed with widely spaced sutures to promote healing and decrease bleeding while still allowing drainage.
peroxide is generally not used or recommended in wounds anymore as it causes too much tissue damage. one old timey remedy i like is soak with hot water and epsom salts. back in 70s an er doc had me soak an infected wound that was just starting to show red lines. not sure why he didn't give antibiotics but the soaking cleared it right up.
seems i heard hospitals are moving away from wet to dry dreesings for some reason. many still use this long practiced procedure but it is changing.
i seen them israeli bandage on ebay not to long ago ... didnt seam like a bad price but i was drinking im sure of it!!!!
the one thing I have lots of everywhere is vetwrap. the downside is that it is latex, so if you have a latex allergy it could cause problems. But for holding icepacks, gauze wraps, or bandages in place with varying degrees of pressure it sticks to itself and is easy to apply the local farm supply sells it for up to $2.00 a roll and it comes in a whack of colours including pink camo which makes my daughters receptive to using it you can't leave it on indefinitely, but for that initial overnight soak in polysporin or similar it works well, is cheap enough to be disposable and light to pack around I haven't tried it, but I would imagine you could use it in a pinch as splint tape as well and no pulling hair or skin to remove it
Here's a good list of what would make a good med kit (very thorough). http://preparednessadvice.com/uncategorized/the-best-medical-kit-i-have-seen/#.UHY0NFGIyNo
Medical care in a SHTF situation is always situational. If you are taking fire from the Opfor then that has to be dealt with - I think for your average situations a ounce of prevention beats a few pounds of cure. Take good care of your feet and practice good hygeine - especially dental. Eat a well balanced diet and stay hydrated and the body does a great job in keeping itself well. Multivitamins are huge in my preps. As are water filters of many types for many different situations.
A 12"X12" piece of plastic wrap will do wonders for a sucking chest wound and takes almost no space. Can be used as an exclusion bandage also.
Bag balm should be in your pack. It's not just for cows! Some people will read the ingredients and freak but it is one of those remedies that has been used for years.