How long does this discomfort in my throat/tongue/under my chin will last due to acid reflux? 1 month and a half taking omeprazole with slight relief.

Another cause?: Usually throat and laryngeal reflux symptoms will show improvement after a month of treatment. If you aren't much better by now then seek another opinion. The location of your discomfort is unusual for reflux.

See a dentist: also. Chronic acid reflux even in mild forms can have very devastating and harmful effects on the mount/teeth.