Feeling faint after swimming in the lake

Depends on how cold the water is, could be initial stages if hypothermia.

Had that happen to me in the summer in an open pool that had rain the night before. Bit chilly when I got it. Got used to it. Got done and then I was dizzy, nauseous and somewhat disoriented for a few hours.

Cold water in the ears triggers vertigo in a lot of people. Choppy water and a horizon that appears to move can also contribute to a kind of woozy feeling, like being carsick. If you're only getting these symptoms while swimming (not while doing other workouts, which would probably be a sign of illness), then it's probably vertigo. A swim cap should actually help a bit, but what would really be effective are earplugs--the silicon kind that you warm up in your hands and then mold to your ears work well. Without the plugs I would be unable to make it through T1 and onto my bike without falling over multiple times after a cold-water swim!

In addition to the info already offered, may I ask if you are wearing a wet suit? That can cause issues...

To help with the possibility of it being the (cold) water in the ears leading to vertigo, - earplugs !

My 3 cents:
1. I recall my first OWS race and thought I something was really wrong with me as I was very out of breath and had trouble breathing in the first 200 yards of the race. As it turned out, my pacing was BAD and I was way over-extended and going too fast.

2. I did an HIM a few years ago at altitude with a water temperature of 61°F. I did not overdue it this time, but when I tried to stand to run out of the water I was really dizzy, and with the rocks in the water, I could not keep my balance and had to pretty much float in, pulling myself along the bottom with my hands. I was still dizzy for a while once I got out of the water but was fine once I got to my bike.

3. Somehow over a period of 9 years my wetsuit "shrunk" . When I got a new wetsuit that was properly sized I realized how much the old wetsuit was compressing my chest, making it difficult to breath. Having a properly sized wetsuit made OWS much easier and more enjoyable.