Thanks for asking in Healthcare Magic.
You seem to be having subclinical (minimal) infection of the laryngo phaynx (throat) called Laryngo pharyngitis. Intake of cool drinks and ice cream precipitates the symptoms. Repeated intake of cold beverages and voice abuse can worsen the condition. Pain while turning to right may be a coincidence.
Indirect Laryngoscopy by an ENT specialist will confirm the diagnosis. If left untreated, it can result in active infection and can lead to hoarseness of voice, severe pain and difficult in swallowing.
You should avoid taking cold beverages. Take warm fluids. Keep the throat moist. Avoid hot and spicy food. Antibiotics like Azithromycin and anti inflammatory drugs like Aceclofenac paracetamol combination will control the infection. Your treating Dr will know about these drugs. Also, warm saline gargle will help in soothing your throat.
I hope this helps. Please ask me if you have any further queries regarding this issue. I will be happy to clarify them.