As with any other sport activity swimming does come with injuries. Though I'm not an expert, I'll add what I've heard and experienced. Probably the scariest would be shouder injuries like the rotator cuff. This could completely end a swimming carreer.
(or so I've heard : )
Lower Back Pain
I used to have plenty of this. I suspect in my case it had a lot to do with short/tight hamstrings. My best advice for this is to do yoga once or twice a week.
Love 2 Do Yoga