Medical Leave in Early Pregnancy

I’m 9 weeks pregnant and I’ve been battling one major cold after another (common cold, stomach flu then sinus infection & now bronchitis). I work in an open room with 5 other ladies so it’s impossible to stay healthy, I’ve exhausted all my sick benefits and just feel like my back is against the wall. I’m overly stressed, exhausted and have lost 10+ pounds. Is it worth talking to my doctor about placing me on short term disability now? (I live in CA)