Do your best and make sure you're honoring your inner conscience.
Other than that, I'm not that interested in having a cure-all for spiritual health and well-being, mostly because I don't believe there is one, especially not one that applies to everyone equally and in all circumstances.
Also, it's worth noting that hand washing doesn't ensure health and well-being. It prevents one mode of infection transmission. It is not a substitute for healthy eating, physical movement/exercise, proper medication, appropriate surgery, access to clean water, meaningful relationships, etc. If I go to an emergency room with appendicitis and the surgeon tells me the most important thing for her to do is to wash her hands, I'm going to ask for a different surgeon. Similarly in church, if I have an appendicitis-like question and someone tells me the spiritual equivalent of making sure my hands are washed, then I'm going to find someone else to talk with.
Lastly, it also amuses and baffles me when people expect healthcare workers to suddenly stop being human due to their profession. Healthcare workers don't have 100% hand washing practices because they're focused on other things, and they are human. They're not purposefully malevolent.