Can you pinpoint the plants in the tank (ie you've had a reaction
from them when they weren't in the tank) or could it be something

My allergist said that I may be allergic to mold growing in and
around the tank (warm moist conditions).

Or it could be some chemicals in the tank ( fertilizers?).

A few great quotes from my allegist:

You can't be allegic to something you've never been exposed to (I
LOVE this one)

Your dermatologist was treating the symptoms, we try to find and help
you avoid the cause!

Try wearing gloves when you work with the tank. Also wash your hand
thoroughly with warm water and soap after every exposure to the tank.
See if it helps. Allegy doctor visits can be expensive. See if you
can figure it out first. If the problem doesn't stop after a week or
so (or gets any worse!!) you may want to have a skin culture done to
rule out bacteria/infections. Also you may want to dreg up a copy of
AFM that had the article on the infection you can get from (was it
Fish TB?) if the pictures look anything like what you've got, get to
the doctor and bring the article (he/she may not have heard of it

Good luck