Translation:I swim at a pool.
The pool can specify a location where there are usually multiple pools. Where I live there is a place where you can go to swim called Moana Pool - but there are in fact multiple pools there. It is perfectly natural to say in English "We swam at Moana Pool on the weekend" or even "We swam at the Pool (meaning a location with multiple swimming pools) on the weekend" - in this instance you wouldn't say that you swam in the pool because you are referring to the location - the place that has lots of pools for you to swim in - rather than a specific pool at the location itself. One final example - On the weekend we swam IN the wave pool (specific swimming pool) AT Moana Pool (location).
No because it would either mean that you swim to the pool (ie. the place, not the physical pool itself) or that you swim in the pool. で is being used in this sentence to show the location where you are swimming - hence I swim AT the pool - ie. the location, the place where there is a pool or multiple pools even. Here's another example of で used in this way - 学校 で 会いましょう！ Let's meet at school! (or at the school)
You can also say in Japanese - I swim in the pool (puuru ni oyogimasu), but that's not what the Japanese is saying here. Puuru de oyogimasu - I swim at the pool (de shows that the pool is the specific place that the speaker chooses to go to swim). Some examples eigakan de eiga wo mimasu - I watch movies at the movie theatre, resutoran de tabemasu - I eat at a restaurant.
To elaborate on what Ana said, normally the sentence would have "<noun>は" in it somewhere to indicate who is swimming.
But when the context indicates it, you leave it out. DuoLingo usually treats "I" as the context, so always assume that.
One way or the other, your answer would be incorrect because the Japanese sentence tells that someone is swimming. No は? Then "I" am swimming.