I just had a thought. We know arrow and bullet wounds have a nasty tendency to occassionally drive clothing material into the wound and fester later. Wearing a gambeson or arming doublet has to increase that risk tenfold when you have many layers of material that could be driven into a wound if it penetrates. So, since the common guy can't afford a silk gambeson, you can't really go without the gambeson since it might save you from a quicker fatal wound, but then you risk slowly rotting later if you incur a non-fatal wound that goes gangrenous. Choices, choices. Man, it had to such to be a poor soldier in those days when your best affordable choice for armour becomes your worst enemy.

Cleaning the wound was probably a technique they quite mastered, since so many of the wounded survived. How else can you explain people surviving horrible wounds like loosing an eye due to an arrow, or amputated limbs…

Heavy gambesons (or even better, many layered jacks) were in my opinion quite protective to most of the long distance shots, where arrow looses a lot of energy due to drag. And if they were quick, there were not many opportunities for close shots.

And I don't know if presumptions from bullet wounds hold for arrows – they’re much more acute, so they would pierce the linen, not drive it into the wound.

I think dirt on the end of arrows could be much more hazardous than a small piece of linen or other clothing material.

With most arrows, bolts and puncture wounds it shears through the fabric from what I have seen with testing on gambesons and such. The bullet no doubt did what you are thinking about, not arrows. The 16th century way to cure this was burning oil dripped into the wound. There are a number of books on medeival wounds, if you find the new book on towton it has a section on it. Now in the great warbow it talks about the copper solution used in the glue on the arrows poisoning people though....

RPM

I doubt that linen represents any kind of serious infection risk. Cotton sponges can be left inside of people without harm. Clearly it would be better for it to be clean linen, but sweat is not infectious.

Dirt from arrows stuck point first into the ground would be a greater infection risk. Puncture wounds in general are considered a high risk for infection, because they drive external bacteria into the wound, and because they do a good job of breaching a persons most effective part of their immune system, the skin.

A significant portion of infections stem from the bacteria naturally and constantly present on a persons skin. Which, when given an opportunity of reduced immunity, can take hold.

/brain rummage

the layers of linen also cause friction... slowing the arrow down from its full force. linen in gambisons would be the same linen that they would pack and wrap wounds with to stop bleedings etc.