Can someone find out why I have been coughing for 3 months?!

You have virtually hit the nail on the head. This is related to asthma, though it may not indicate a general recrudescence of your childhood condition. You do need a chest X ray to exclude rare causes of prolonged cough, but this is likely to appear normal. The odds are that you have developed post viral bronchial hyper-reactivity. Basically your lung respiratory mucosa has lost its stability. Asthmatics do this with every cold, but the rest of us can do it as a one off. Generally it does eventually settle on its own, but after 3 months inhaled steroids should be used to restore stability. It is likely that a 6 week course might be adequate and then having returned to normal they can be stopped. However occasionally, especially in someone with a history of asthma, this is triggering for the return of the the condition, and when inhaled steroids are discontinued symptoms quickly return, indicating that more prolonged management is required.

GP for more years than I care to remember

You may have had a sinus infection and need antibiotics to get rid of it. Definitely see a doctor. If that's not the case then you may have allergies or it very well could be asthma related. I know that allergies can cause post-nasal drip which can cause long termed coughs. You can see an allergy doctor and get tested.

My own life experience.

The general rule I remember is 'if you are coughing for more than two weeks, think TB unless proven otherwise'. Anyway, it is better for you to see a doctor to get a more accurate diagnosis.