Hi, welcome to the forum, allergy shots can be associated with flu like symptoms. Other wise it can be a sign of upper respiratory tract infection or sinus infection secondary to influenza virus A and B, parainfluenza, coronavirus and human metapneumovirus. This can be complicated by bacterial infections. If bacterial infection is suspected then appropriate antibiotics will help.
Otherwise pain killers against prescription will give you quiet a relief for your headache. If you are having sign's of allergy then oral anti histaminics will relieve the allergic symptoms. The dose allergy shots can be reduced. You can discontinue, if you it is intolerable. I suggest you to consult physician. Take care and regards.
It could be a reaction to the shot, but it could also be a cold. Discus this with the nurses before you next shot. You should take an antihistamine before you get your shot any way. That would help. Also, do you do sinus rinses? they are very helpful with these symptoms.
If it is a reaction to the shot, your symptoms should improve with each shot. If they don't, I wouldn't blame you for stopping the shots. Your symptoms are mild (although still and nusance).
Take care and God bless.