HI! I am wondering if I can plug my hot water insinkerator into the outlet that my refrigerator is plugged into. the fridge model sticker says it draws 7.2 amps and the insinkerator says it draws 6.45 amps. the fuse in the control box panel is 20 amps to the fridge. I know that obviously hiring an electrician to run a new line is best, but I am wondering if this can work....

No, it's too much on one line. The refrigerator has to have extra for starting amps.

Better change the line, or you can use heavy silver wire to run both.