Nat, put a pillow on your mother's knees, lay gently across the pillow face down with your chest on the pillow. Have your mother gently thump on your back to loosen the gunk a little bit and cough some of it up. That might help. Or just gargle with warmish water, maybe a little bit of salt or white vinegar to get the ooky stuff out.
And keep drinking fluids and eating popsicles! yay for popsicles!