I'm new to the 3200m race in track. I swam during the winter and wanted to try something new with track. I have run an 11:45 so far. I took it out with the lead pack in 70, 2:30, and 5:31,
You need to get much, much better/smarter at pacing yourself. As others pointed out, you were actually running pretty slowly after the second lap (you averaged 90 seconds/quarter in laps 3-4, that's on pace for 12:00).
You haven't said much about your training, but I'd suggest there isn't much you can do about increasing milage at this stage. Run almost every day of the week, that should get you about 25-30 miles. Don't try to do more than that. Cut back on other exercise, it's counter productive. Better to go for an easy run than a swim.
I think the most important thing is to focus on being consistent your speed work. I'd suggest two workouts: (1) goal-pace intervals: 800m reps at goal pace (2:45 or so), jog 400m between each rep. Do 5 of these. On the first rep, check your watch at the 200m mark to make sure you're not starting too fast. Do the first one at 2:30 and you'll blow the workout. The second workout: steady-paced 5k tempo run. Do this on a track so you can check yourself on pace, and start by trying to hit each lap in 96 seconds. Don't go all-out on this workout -- it should be hard but controlled, it should feel like the first half of a race.
Another point -- 2 workouts may be better than 1. Don't get into the trap of thinking that 3 must be even better, and 4 must be better still. But it's not. Beyond a certain point it increases injury risk without providing much additional training effect. So get in those two workouts consistently, bust your ass on the goal pace intervals, but
go EASY on your easy days (jog your easy runs at about 8 minutes per mile).
Good luck.