My 55 year old mum since having covid twice has developed a cough which she has had for 5 months and morning headaches almost everyday. she has had a lung x-ray and all clear. scared its something serious?

Most likely this isn't serious. It is quite common to develop a longstanding cough after any kind of bronchitis or lung infection, including covid. Is she a smoker? Still, it would be best for her to see her doctor and make sure it isn't serious and/or to get treated. Good luck to her.

Lingering cough and sinusitis have been described in such circumstances and are likely, however other causes cannot be ruled out. Tight follow up is recommended.