No, you'd better not have the exercise right now since you have the broken blood vessels. There will be the bulbar conjunctiva and sclera organization blood vessels under certain circumstances. It may appear into expansion congestion gore or hemorrhage. It can present red whites due to some organization's blood supply source. It must be caused by the dryness of eyes which will cause the eye nerves to work in disorder. And the eyes corneal don't absorb the tear glands fully and cause the blood vessels in the eyes. It is so dangerous if you don't treat it well. You'd better not exercise because there may be the coming bacterium in your eyes to intensify the situation of the broken blood vessels. You should have the good rest for the eyes and drink more water. In addition, you'd better not use the eyes in long time with no rest. You could use some eye drops which mainly target at the blood vessels in the eyes.
Well, as a matter of fact, broken blood vessel could be resulted from a wide variety of reasons, so you need to identify what led to your problem. Generally speaking, you should take some time off to recover and have a good rest, lest some other problems may arise. Of course it seems to be little bit risky. However, if you insist, you should avoid doing some hard sports.
Well, you have no choice but to stay at home and take a good rest. Don't do any exercise, especially swimming. And keep in mind that let your eyes relax, you'd better not stare television or computer in a long time, even read books. The blood vessels are the part of the circulatory system that transports blood throughout the body. Blood vessels play a huge role in virtually every medical condition. When one of these tiny blood vessels bursts, you will notice a bright red or dark patch on the whites of your eyes. If you really get a burst blood vessel in your eyes, you sometimes may feel some pain or mild irritation. But relax; don't rub your eyes, some kinds of blood vessel bursting can be treated without any medical treatment. So if you find you may get a burst blood vessel in your eyes, visit a doctor as soon as you can.