That's weird to have a rule about don't swim in a lake!! Unless you live where there are alligators.
As a kid, I had a recurrent nightmare where I would start swimming from the "point" (penninsula) at our lake cabin, to try to get to the other side of the lake. This was our usual swimming spot, but of course we never swam across. There was either the drop off, with a nice stone bottom, unless you went out far enough to get to where the weeds were, and it was very daring to swim down and grab one- (like 10/15 feet?) or the sand bar, which was shallow and had clams to catch for fish bait. Anyway, I would start swimming, and eventually become entangled in weeds, in the dream, and wake up. I _always_ had this dream.
The thing that cured me of my fear of weeds was scuba diving in those lakes, with 10 feet vis on a good day, and getting relaxed about swimming among the weeds, with the fish. I also did some diving looking for artifacts in lakes, along mud/muck bottoms, in near-zero vis. You have to build up gradually to get used to it- I mean in worse and worse visibility, and it was still pretty easy for me to get spooked if I allowed my mind to go there.
I think in your murky lake, if you can practice ahead of time and get used to the feeling of the weeds touching you, that will help a lot. If it can become a familiar and non-threatening feeling for you. I think this can only be done by repetition, and you have to mentally control yourself to think "friendly" thoughts about the weeds, not scary thoughts.
I did a tri last summer in the ocean, in a bay, where it was just about zero vis from the brown mud/muck bottom. I did practice swims there almost every day the week before to get used to the crap vis. It's freaky to swim and have things touch you that you can't see.
Good luck!!
Nanci
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"...I'm like the cycling version of the guy in Flowers for Algernon." Mike Magnuson