There are several solutions to your problem:
1. Yes. Laminate it, but stay away from gloss laminate. That will repeat your problem. If your printshop can put a hotmelt laminate on it, that is recommended. Ask for something called "deep crystal". This should be applied on both sides to prevent bulging. Never use one-sided lamination on paper, hot or cold !
2. Reprint it on complete matt paper. Not the best solution, but better than gloss and semigloss. The plexi will bring back the glossyness.
3. Reprint it on self-adhesive vinyl and coat it with a cold structured "crystal" laminate. If your printshop knows it