That's funny... after I posted, I thought to myself that I should've added... "unless, of course, you're allergic to latex!"
Yeah... the non-latex gloves are fine too. I've used both. You're just looking for something that doesn't have any powder or additive, and are inert.
Since you obviously have allergic issues already, I'd definitely be using gloves in your situation. Here's a source for long shoulder length gloves:
I own some, and *think* they're non-latex, but if you're interested give the guys a call and ask for sure. (Really nice, helpful people at that place.)