Dual II's label has interesting information. It's looking like various types of petroleum solvents from top to bottom. It says to flush the skin with water for 15 to 20 minutes. 

At the very least, some of the components of Dual II could cause psoriasis. 

Here's the MSDS from Syngenta:

http://www.syngenta-us.com/sds-label/dual-ii-magnum

I would recommend printing this out and taking it with you if you see a medical provider, so that they know what is in the Dual II. There's specific information on pp. 3 to 6 that applies to exposures.

2,4-D was probably the amine formulation, and that's just an amine salt in water. The Dual II has several forms of petroleum solvents and cyclic compounds that look more apt to cause skin irritation.