Is it possible to be allergic to wood plugs?

well, there are actually a few things that could cause this, wood of course can splinter, and your body will naturally try everything it can to expel it. Also, yes, anyone can be allergic to anything. If it continues and you are seriously concerned about it, you may need a doctor to prescribe some antibiotics to help kill whatever bacteria has gotten in. Also remember, this is the body's reaction to anything foreign that it is aware of, and if it is something serious, it will not stay with just the symptoms you described, it will start trying more and more methods to get rid of it, and you'll generally feel like you've got some sort of cold or flu. Keep that in mind over the next few days/weeks because if you do start to feel achy or sick in any way, it's very likely they are connected. Good luck.