I recently had a chest xray during a viral infection. The results showed "prominent interstitial markings bilaterally." what does this mean? Worried!

Depends. Depends on other health issues going on. Chest xrays w/ prominent interstitial markings include a large variety of abnormal processes such as inflammation, edema, lung disease and environmental exposure. A viral infection could certainly explain your xray, however, if your respiratory condition persists, i would follow-up with a physician.
Interstitial marking. An infection alone can cause the pulmonary markings in the lungs to change. More than likely that is the cause. If your doctor thinks a follow-up x-rays necessary then i would make sure to follow-up. If nothing else showed up and you recover without incident then that may not be needed. Check with your dr.