They are likely legitimately concerned about your mental wellbeing. Actual sobbing in the workplace over a work problem would normally be a pretty clear signal that someone is one the edge of a breakdown. If this is a regular coping mechanism for you (as you indicate in comments) then communicating that to Tom and Bill is definitely in order.
In my opinion the best course of action is to arrange a one on one with Bill and advise him that this is not unusual behavior for you when you are alone, that this helps alleviate minor sources of stress. Be prepared for him to be skeptical as this is rather unusual behavior however being sincere and open is likely in your best interest here.