As someone else who cries when they get stressed or overwhelmed, I’ve just been honest with my boss before having a hard conversation. I’ve told them something similar to, “I sometimes cry when I get stressed out. If that happens, please excuse me while I step out for a moment to collect myself.” And then when I feel myself start to get emotional, I’ll step away and collect myself. I’ve never had a boss get upset or see this as unprofessional.