Please help! I have red veins in eyes become more irritated?

A few possibilities. This could be due to allergies, dry eyes, or eye infections. All can start or affect 1 eye first. The treatments are very different. For allergies, zaditor (ketotifen) is a good otc eye medicine. For dry eyes, lubricating tears are necessary. For infection, usually of the eyelids, start with eyelid warm compress and diluted baby shampoo scrubs. You should have a baseline exam with your eye doctor.