I was exposed to mold spores at work, and now I'm sick. Can I ask for sick pay or lost wages?

Yes. Assuming you can prove this occured on the job; then it should be covered under worker's compensation. Check with your hr person at work.
You can make a claim. It is a difficult case to support, but there are certain people that are susceptible to health problems from mold. Usually they will have immune system problems or severe respiratory disease. Even then it takes evidence of exposure and proof of harm. With that said every employee is able to make a claim if there is a concern of workplace harm.
Sick building syndro. Very difficult to prove and has no real epa approved testing parameters to go off of. An occupational health physician might be better able to answer your questions.