If I Inhale Bleach, During Cleaning For Example, I Get

If I inhale bleach, during cleaning for example, I get a massive headache and the smell of bleach stays in my nose for hours after. If I get bleach on my hands it triggers my eczema and they will break out in tiny blisters and peel over the next couple days and weeks. I have read that there is no true "bleach allergy" is this true? What do you think is causing my symptoms? I'm especially curious because I just had a root canal and the cleaning solution the endodontist used smelled of bleach. I asked him if it was bleach and he said it was similar. I went home and did a web search and all the info I gathered confirmed that dentist do in fact use plain bleach to disinfect during a root canal. Could this harm me if I have an allergy or sensitivity?