Swimming and pilates are certainly good forms of exercise - I think that without being blunt, if you have been told that you have to limit your exercise to swimming and pilates, then what choice do you have? It's either swimming or nothing and swimming is certainly better than nothing, so my advice from that point of view is go for it.
You will find that swimming is very different from activities like running and cycling, because the water and the buoyancy effect mean that you don't work against gravity to the same extent. It's also very technique reliant, and so until you develop a decent technique, it's difficult to get the benefits from swimming, whereas running you can pretty much benefit from the get-go. HOwever, once you establish a regular swimming routine, it's very easy to get great training sessions and some really good workouts. What you are swimming now is good, but you can begin to build this up over the next few weeks and get to a kilometer a day of swimming. The other thing is to do intervals, which in a pool is really easy, because you can swim two lengths hard, two lengths easy for example.
I do suggest however, that you get the back sorted out so that you can begin to return to the activities you had, if you are not currently doing this already.
The information provided does not constitute a diagnosis of your condition. You should consult a medical practitioner or other appropriate health care professional for a physical exmanication, diagnosis and formal
advice. Health24 and the expert accept no responsibility or liability for any damage or personal harm you may suffer resulting from making use of this content.