I'm wanting to get my belly button peirced but i'm going on vacation less than 2 and a half months will i be able to swim in the ocean ?

Yes: Provided that you research the tattoo parlor for reputation, ask about the tools they use and how they are sterilized, and do good post procedure wound care the skin should be healed completely in 6-8 weeks at most.

Navel piercing: Sometimes may take more than 6 months to heal due to friction and like any open wound infections can occur as the ocean is not sterile ( though the salt may provide some protection- lakes are worse). To be cautious may wish to defer as one can not be sure how it will heal. Discuss with doctor/urgent care

Yes: 3 months is plenty of time for it to heal. keep it clean and dry