Hi, I understand how painful watching your child cry each time can be; however, you mustn't let the crying stop you from taking your child to swim lessons. I'm not sure where you live; however, I elected to take my son beginning last year at age 4 to a private swim instructor.
She takes children as young as 8 months and up to age 8 in the younger child class. She takes about 6 children at a time and they rotate through. The lesson lasts for about an hour and 15 minutes. I have observed some children cry the entire two weeks, and I have observed some cry at the beginning, but then stop.
With that said, each one of the children who go through her class are able to swim by the end of the two week period. She guarantees it or there is no charge. In order for them to graduate, they must be able to be thrown in at the deep end, turn around, and pull themselves out. I have never observed this with the 8 mo old children, but have with children as young as 11 mos. It is absolutely amazing to watch. Her philosophy is that she wants them to be able to get out of the water in the event they accidentally fall in. With her lessons, she only requires one day of parent in the pool. Depending on your location I would be happy to give you her name. She's listed in the phone book, but doesn't advertise. All of her clients are based on referrals.
Back to your original question, should you keep it up. Absolutely, it could save your child's life.