in the future, at the design stage, if it can be vector, it should be vector.. I don't know how many times I've told a client to go find the vector, because if it was done by a "real" designer, there will be a vector... not to get into whatever the heck "real" means... but as a sign guy, anything I design (even if it's for an iron on T that I print 4 color process from a bitmap) there is always the chance for a need to produce that image LARGE... so, as I said... in my opinion if it can be vector, it should be vector!
Also, show it to us. If there are only solid colors, with high contrast, using the magic wand to select, cut & paste to new layers (or just select, create new layer, while selection is still intact, fill in new layer, then delete from original) once each color is isolated, select, create path from selection, export paths to illustrator..
so, post the design, if you can do it yourself, we'll help... everybody learns! (& I'm sure there are better ways I can learn too... so, I'll be watching here.