Are both OK: Same here. I'm going to the gym too.
And
Same here, I'm going to the gym too.
They are both OK. Very strictly, I suppose the second one might be objected to as a comma splice, but I think most people (almost everyone) would accept it.
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They are both OK.
Very strictly, I suppose the second one might be objected to as a comma splice, but I think most people (almost everyone) would accept it.