My employer painted our office and the chemicals made me ill. I was weak in the legs, had breathing problems and a hoarse voice. I immediately notified my supervior, who called Human Resources. They sent me to one of their clinics and the physician recommended that I work at the other office until the fumes were gone.
By law your employer must do something. I would notify Human Resources immediately. I believe this is also a Workman's Comp issue and if you miss any work because of this, they need to pay for your lost days.
In addition, I thought that I would mention that there are some very good homeopathic remedies, including remedies for people who have reactions to chemicals. It is just a thought and something you may want to check on the internet. I have a bottle labeled "Household Cleaners" - which helps me when I'm around bleach and other chemicals.
I feel for you. I have a severe allergy to Bleach and require an epipen after being in close proximity to the fumes. This allergy began a few years ago and has progressively gotten worse, I can't even be near or in a pool that has recently been chlorinated. I empathize with you. I would like to find cleaning alternatives as well.
Breathless due to toxic fumes
I recently became aware that I cannot use any strong cleaning products in my apartment. PineSol is great for cleaning the cat litter box, but the fumes are so strong that they give me an allergic cough and I cannot breathe. A little bit of this and I am wheezing and coughing. I have subclinical asthma (so I have been told) and I guess my immune system reacts violently to these things. I am throwing out the PineSol and will never use it again. Same with bleach or anything else. I just cannot be around it. I have also had this problem after being around fresh paint--I cannot stand that either.
I have problems with all the above as well. For the cat litter box I recommend Nature's Miracle, which you can get at a pet store. Do not get the one specifically for cats--that one is very strongly scented and made me sick. The original version (just called Nature's Miracle) has a slight scent that goes away when it dries. (Normally I can't tolerate ANY scent, but this one I do okay with.) The cat "scent" will go away when it dries as well. It is for anything organic (those things a cat will do on the floor, as well as blood). It will even work on dried stains.