The more the whale swims, the longer it lives and it does not mean that the whale will become thin. This is called the other side of the coin.
You will do it, it will take time... anyway swimming is a life saving skill and it takes time to learn the skill.
My story is that I am scared of swimming in the lakes situated in the Himalayas, firstly these lakes are situated above the tree line and secondly the water is very cold. As soon as I enter the lakes, my heart rate goes to 180-190. But I always enjoy swimming in the lower range.