OP - I think you over-reacted too, and I can't help wonder where your 3yo was while this was happening? It sounds like your DS was in the normal pool? Alone? As in you weren't standing there with him? If that is the case, the life guard was well within their rights to ask you to supervise your child more closely. At 13 months, being over-confident in water is NOT a good thing. One slip is all it takes. Kids drown quickly and quietly whether someone is watching them or not. Unless you are right there to grab them, it could be too late. My DS is 2 and confident in water, but there is no way he would be roaming the shallows by himself whether he wanted to or not. It's just too dangerous. I may not hold him the whole time, but I would only be a step behind him.
Even if you were right there, the LG was only enforcing the pools rules. And looking out for your child. I think you should be grateful that they were and not come on here and flame them for it. If the LG was "watching you like a hawk" I'm sure it wasn't out of spite or malice. They would have assessed that your child was at risk and were watching accordingly. Therefore doing their job.