If you can't pass a Navy PRT, ahhhh.... yeah. That should be the last of your worries. I'm like 20 lbs over weight and pretty much never work out. Still max all but the run, and that's still like 10:30. If this were the Marines, different story.
Now I don't recommend going to OCS out of shape, like I currently am, but you will be amazed at some of the people who show up with you and make it through. One dude in our class lost 30 lbs and is now "flying" jets in Meridian.
API APIT is the same as a normal PRT, it's just on a chip trail rather than a track. Which I actually prefer to run on. You'll take it when you first show up before you start IFS. They won't let you start flying until you pass it. I highly recommend passing the first time.
If you are a decent swimmer, then your biggest worry will be getting a blister from those god awful 20 year old boots you'll be barefoot in.
Now the helo dunker, some people think it's a blast, but fuck that thing. If you're not on a SEBD, no. thank. you.
To prep for OCS, spend time with your family and friends, study your OCR, and put down the video game controller and do something active. Sure if you suck at swimming, spend some time doing laps and treading water, maybe even wear heavy shoes.
Good luck!