I went swimming tonight, which iwas the fifth time this week.

Though my back felt sore after I swam 30 minutes, I didn't want to stop because maybe it wouldit might be the last time I wentgot to swim this year / it might have been my last opportunity to swim this year.

Summer is over, and I will be busy in mywith work for a long time.

Your original sentence was fine, but this is a bit more natural

When most people left the pool to go home since it was nearly the time which the pool would be closed, there was only me swimming in the poolit was almost closing time, everyone but me had left to go home; I was the only one there still swimming.

Your original sentence is grammatically correct, but quite heavy

It became quiet, and shiningy because of the light.

I immediately felt very peaceful all of a sudden.

"All of a sudden" sounds abrupt and contrasts with the idea of peacefulness in my view. This is a subtle correction, however, and your original sentence is also fine.

I felt like I owned the pool privately, so I swam slowly and relaxingcalmly.

Or "It felt like it was my own private pool"

"Relaxing" doesn't work here as it's an adjective, and "relaxingly" sounds weird as an adverb, so "calmly" should capture the sense you were trying to achieve.

I becomcontinue to love swimming more and more.