Pain in the throat especially during the intake of cold beverages can be due to a multitude of causes. It could be as simple as a general intolerance to cold beverage or a pharyngotonsillitis.
Do get evaluated by an ENT who will find out the root cause of your problem
The post nasal drip
can also be indicative of an underlying sinusitis
which can aggravate and/ or cause the throat problem. An ENT consultation with a full evaluation including diagnostic nasal endoscopy
and CT of the sinuses