We just brought DD to the beach for the first time this weekend! We of course waited until it was cool enough (about 6-7pm). We dipped her tootsies in the water and in the sand and rinsed her off really well afterwards. It's been a few days now and she's fine. She loved the beach!
Re: 2 months to early for pool/ beach
I would only bring him in if the water is warm enough and I would probably rinse him off well afterwards. The water here is waaay too cold!
I am sure pool water is fine!
My DS got in the pool with us at exactly 2 months. He wasn't in there long. We bought him a shaded float also... it's recalled now