Can you get food poisoning several days in advance and not show symptoms until later? ?

My boyfriend and I just got back from cancun. On Thursday night me, and three other women got extremely sick. Throwing up, uncontrollable diarrhea, very very acidic stomach and cold sweat, no fever. We threw up all night. And then the next day was feeling much better, however not 100%, more like 65-75%. Im still not feeling 100% today, very acidic stomach still and stomach pains. We thought it was food poising but, now I wonder if it was because it's still in my system. .... And now my boyfriend just started to throw up. Any ideas as to what it is?? And how to help fix it! Thanks