Thank you for your question. I would need to understand your symptom better as the throat is a symmetrical structure and moves symmetrically (right and left sides) on swallowing. Since you mentioned that you have a "flu" a few weeks back and it appears to be coming back, there is a possibility that you may be feeling the mucous from the back of your nose flowing down the back of your throat (maybe more on the right side), hence giving you the feeling that your throat is "moving to the right".
The other possible reason for a feeling that your throat is "moving to the right" is an abnormal growth in your throat or neck region.
I would suggest getting your throat checked by your General Practitioner first. If there is a need, he/she will refer you to an ENT Specialist for further evaluation.
Hope this helps and all the best.
