Hi..
Welcome to HEALTHCARE MAGIC..
I have gone through your query and can understand your concerns..
As per your complain it  seems that itchy throat along with cough can be due to Upper 
Respiratory Tract Infection also known as 
Common Cold..
Getting cold one or twice an year is not an indication of poor immunity as it is not abnormal and people can experience it commonly..
I would suggest you to take anti allergics like Levocetrizine, anti inflammatory painkiller like Ibuprofen, do warm saline gargles and steam inhalation..
Take cough suppressant containing 
Dextromethorphan..
Chew a Vitamin C pellet and suck throat lozenges..
In case if you develop cold and phlegm also take decongestant like 
Phenylephrine and Mucolytics like Ambroxol along with above advised medicines..
Avoid spicy and chilled foods, sip water water and take a 
soft diet..
Hope this information helps..
Thanks and regards.
Dr.Honey Nandwani Arora.