Yes it is possible to have soreness towards one side due to reflux. If it's not the first time, I suggest you to consider a review and change to your diet with consulting ENT for medical management of symptoms. However, you should also visit a dietician if you think it is long standing problem.
Next Steps
Visit an ENT nearby, consider visiting a dietician (not compulsory though).
Health Tips
Medicines only reduce symptoms. If you don't change your diet according to your stomach and body's need, medicines might not help in the long run.