Focus on the 'excessive' aspect, which highlights irrational or unnecessary concern for health. Even a minor headache makes him run to the doctor; such a hypochondriac.
Pro Tip 2/3
Perceived Illness
Understand that a hypochondriac believes they are sick, even when medically healthy. I told her it's just a cold, but she's convinced it's more serious — typical hypochondriac behavior.
Pro Tip 3/3
Not an Insult
Be careful using 'hypochondriac'; it can offend if someone actually feels ill. Calling him a hypochondriac wasn't nice; he was genuinely feeling unwell.