El cuerpo y la salud

You do not have a headache in Spanish. The head hurts you.

Me duele la cabeza. The head is the subject, you are the object, and the verb agrees with the body part rather than with you. Two things hurt and the verb goes plural: me duelen los pies.

This is gustar all over again, and it is worth noticing that the two hardest constructions for an English speaker are the same construction.

The article, not the possessive

Me duele la cabeza, not mi cabeza. Spanish uses the definite article for body parts almost everywhere, because the me has already established whose head it is. Saying mi cabeza is not wrong exactly, but it sounds like you are distinguishing your head from somebody else's, which is rarely the point.

Same with washing, dressing and moving: me lavo las manos, not mis manos. English needs the possessive because it has nothing else. Spanish has already told you.

Three ways to be unwell

Estar enfermo is to be ill right now. Ser enfermo is not a thing you want to say. Estar malo also means ill, and ser malo means to be a bad person, so the ser/estar split is doing serious work here.

For the doctor, both médico and doctor are used. Médico is the profession, doctor is the title and the form of address. You see el médico; you say gracias, doctor.

cara

Cara is the face. Caro is expensive, and the feminine cara is identical to the noun. Es cara can be it is expensive or, given the right sentence, she is a face.

Context sorts it out every time. It is still worth knowing why the sentence briefly looked strange.