I actually spoke with my therapist yesterday about being concerned about stopping worrying because then I'll "miss" a symptom, and she reminded me that even if I stop worrying about my health to an obsessive extent (to where it's truly a disorder), I'm still going to be very vigilant about my health because my time with hypochondria has me wired that way. Working out your problems won't let you "miss" something - it will allow you to be logical while being vigilant and not have the fear and panic attached to it.
Stopping Googling has helped me a lot. I also like to use self talk, sort of like being in a third person conversation with yourself to disprove your anxious thoughts. For example, consider starting to worry about your fingernail cracking. (Something that sucks but isn't lethal - don't want to stress yourself too bad). Now - picture it in your head. Think about how terrible it could be. Imagine everything it's be like to have your fingernail crack. Now, don't worry about it. Forget about it happening. Give yourself a couple hours to focus on something else. Then look at your fingernail. Has it cracked because you stopped worrying about it? I bet not! Same works for blood clots and other disorders when you attach superstition to them.