Some serious and not-so-serious medical conditions have fingernail manifestations. Examples include psoriasis and endocarditis. The serious illnesses would have other symptoms that are not subtle. Things like psoriasis are not life threatening, and are thus only treated if the symptoms are troublesome (most would argue that unsightly fingernails, if that's your only symptom, is not worth the treatment).

Many times curved, peeling, or discolored nails are just that. We don't necessarily know why, but it is of no consequence. You were right to consult your doctor, and his or her diagnosis is probably right. If you are still concerned, get the second opinion of a dermatologist.