Definitely not. If you go swimming, the germs will easier invade in the eyes and things may getting worse. And the bacteria in your eyes also easy to run into the water, it is not good for other people's health. Generally speaking, the stye may disappeared after 4 or 5 days .You can use a damp and hot towel on your eyes for 20 minutes everyday and it will help you recovery, then you can go swimming and have fun.
If you got stye in your eyes, you'd better not to go swimming. You know, the water in swimming pool contains of many bacterium that will make the stye in the eyes more serious. So, if you want to recover from stye soon, you'd better not swim at this time. You'd better get eye doctor to treat the stye in your eyes. Wish you will recover from stye soon.