Swimming

I could not swim. My husband taught me swimming. It was our first holiday together. We went to the Black Sea. There It was wonderful there! I take took a fancy to the noise and smell of the sea as well as its his power. I wanted to swim like as other people did. But I feared a the water was and a deep. My husband urged me to try. He became my trainer. It was not easy. But I did it! At the end of holiday I could swim. swum. Of course I did this not very well.

Other ways to say this include:

"Of course, I was only a beginner"

"Of course, I was only starting out"

"Of course, my level was not very high"

My fear of a deep water was had not disappeared.

Therefore I was swimming along a coast that any time to feel a bottom.

Did you mean to say something like this:

"So I was swimming along the coast, knowing that at any time, my feet could be touching the bottom of the sea"

But it was really good swim and I enjoyed this pursuit. action.

Swimming

I could not swim. My husband taught me swimming. It was our first holiday together. We went to the Black Sea. It was wonderful! I took a fancy to the noise and smell of the sea, its power.* I wanted to swim like other people. But I feared the water and the deep. My husband urged me to try. He became my trainer. It was not easy but I did it! At the end of the holiday I swam. Of course I did not swim very well. My fear of the deep did not disappear. Therefore I swam along the coast where at any time I could always feel the bottom. But it was really swimming and I enjoyed this action.

*normally you would call the sea 'it', but  poetically you can call it 'he' or 'she'. In the English speaking world it is 'she'.

You begin to swim. You began to swim.  You have swum. You swam. You have begun.

very well written!