The problem is that your brain is more likely to believe information you just read and starts actively looking for confirmation. You read about stomach pain in some rare disease - and suddenly any discomfort feels like proof. What helps here isn't just avoiding medical websites (though you should do that too), but consciously redirecting your attention the moment panic kicks in. When you notice you're searching for symptoms again, try doing something physical: go for a walk, do some cleaning, anything - the point is to distract yourself for 20-30 minutes.
Second thing - make it a rule that only doctors diagnose, and if something really bothers you, you don't sit around on the internet but just book an appointment. This removes the uncertainty that feeds the fear. If you don't have symptoms - you don't check. If you do - you go to a doctor, not Google at night. One more thing: news about diseases usually covers rare cases because that's what's new and scary. The odds that you'll get some exotic disease stay the same whether you read about it or not. But your brain forgets that.