Seeing as most of us have great imaginations, we can all contribute.
My suggestion is similar to Nosferatu's. However different in its own way.
To start, I'd first assess what my costume entails (which you have). After that. I'd do a sketch of various ideas.
So I'm gonna go with this as my suggestion.
For the face, keep it gruesome. Your coming from a large chemical, possibly nuclear spill. I'd put the "Nuke" or "Biohazard" label on a yellow or white jump suit. A painters suit would be a good starting point I imagine. But make it like a suit that handles serious chems, as well as hooded.
A ventilator mask would be a solid idea. I mean. You don't want those chemicals in your system. I'd go with Nos's idea of having a break on one side, showing exposed, and chemically burned skin. As best as you can afford to.
Rubber or large boots are a must. Chemical handlers need that sort of thing. However. Zombies aren't prim and proper. So I'd make it look like you spilled something on them and the suit. Green glow in the dark paint of you can find it. And be liberal with it. I'd also ad a bit of red paint for a blood effect.
Large, black rubber gloves. Also with paint on them.
Lastly, I'd see if you can find some paint buckets you can mark with a Biohazard sign or a nuclear warning label. That way you can add to the whole theme.
Thats my suggestion anyway