Lately, my eyes have been itchy and there's a slight burning sensation as well. I occasionally see floaters and my vision goes blurry (however, the blurriness goes away as soon as I rub the eye). I'm thinking that maybe I have uveitis. Would this show up on a brain MRI? Thanks.

No, uveitis would not show up on an MRI of the brain. It is an inflammation of various parts of the eye (anterior, posterior). It would be detected in an exam conducted by an optometrist or opthamologist.