Is spring pinkeye infection or allergy?

Either or both. Tree pollen in the spring often causes itchy, red eyes (allergy) and can be treated with avoiding outdoor pollen, taking an antihistamine by mouth or allergy eye drops (otc or rx). If the redness is accompanied by pus or pain then infection is most likely. Often people with itchy eyes rub them for relief and cause an eye infection on top of their allergy. This requires a call to you doctor.
Hard to tell. If it happens every spring, starts in both eyes equally, and correlates with the tree pollen counts in your area, it is probably allergy. I always prefer to take eye symptoms seriously - vision is important! you should get it checked out by your doctor or an allergist.