Hi Helen, that was a good effort. I think your title was meant to mean:

"The Old Lady Who Swims"

Some more suggestions:

Swimming administer to people's health.  

Swimming improves people's health.

Swims to the midway is very tired, but can't stop.

I get tired swimming to half way, but I can't stop.

I must admit i'm impressed the swimming's Aunt.

I must admit I'm impressed by the old lady who swims.

The swimming's Aunt.(?)

Every time I go swimming, I often meet an old Lady.

(I think the lady is not one of your relatives, then you cannot call her 'aunt'.)

When I go swimming, I often meet an old Lady.

She swims faster than I and she do not take a rest. One day, I looked up at her and said :

"Madam, you are great, we young people cannot swim better than you." The Lady said, "I swim every day and every time she swims for an hour. Swimming is good to people's health. Swims to the midway is very tired, but can't stop.(*)"
I must admit i'm am impressed by the lady.

* While swimming, I feel tired but do not stop.

The swimming's Aunt.

Every time I go swimming, often meet an Aunt. She swims faster than me,without rest, I look up to her. At one day, I ask her:" Aunt, you are great, we young people do not swim as you as well." The Aunt said, she swims every day and every time she swims for an hour. Swimming administer to people's health. when swims to the midway is very tired,
but u can't stop.
I must admit that i'm impressed the swimming's Aunt.