Close your Ears...!

Do you experience dizziness when you swim in Open Water?
Well, here's why.
Cold water in your ear stimulates something called the Vestibular-Ocular reflex, this in turn induces Nystagmus. This reflex makes your eyes micro-beat incredibly fast and to the opposite side to which ear the cold water is in.
This is called Caloric Testing. Interestingly, this is also a used as a test for Vertigo.
What's this got to do with my Open Water Swimming? Well, swimming and cold water ending up in both ears is likely to upset that system, possibly even making the reaction excessive.
That excess reaction will manifest as dizziness, in some cases, nausea; imbalance is common too. Think motion sickness and you have the same feelings.

Personally, I have worn ear plugs whilst surfing, swimming, kayaking and other watersports for a long time, so as to prevent Surfer's Ear, but they also help reduce ear infections and the effects mentioned above.  Ear plugs can be purchased off the shelf from swimming shops, amazon, wiggle etc. However, if you really want to protect your ears and dramatically reduce the chances of the occurrence of the Vestibular-Ocular reflex and Nystagmus, then visit an audiologist and have some earplugs made that are specifically moulded to your ears. Specsavers have this facility, Surf-Plugs will send you a moulding kit, or they can even be prescribed on the NHS.
It is very much worth it, if nothing else than to prevent Surfer's Ear, Swimmer's Ear and the other names that describe the body's mechanism for blocking out water from the ear canal by growing more bone in the canal to narrow it. The solution, crudely speaking is an operation with a drill, maybe a chisel as well! 
Below is the link to a video that shows just what's required to undo bony growths, exostoses.
https://www.youtube.com/watch?v=GXJzDaqmpoo