My mom and I both work in a hospital setting and we are both allergic to latex. My mom is also allergic to the soap that our facility uses. Each of our nurse managers orders us our very own latex free gloves to use and my mom even gets her very own soap. It's sort of pain in the butt, though. We have to stuff our pockets with gloves and/or bring our box of gloves with us, and my mom washes her hands at certain sinks that has "her"soap. Except for an isolation patient: then she just leaves her soap in the room so she can wash her hands before leaving. But even with the inconveniences, it's MUCH better than the reaction that occurs.
Anyway, my point: don't give up!