Do they make scuba diving head gear that bring oxygen to the mouth and nose? It would be easier for me to breathe out both my nose and mouth if possible.

Yes, though you will be most likely breathing air (21% oxygen, 79% nitrogen)…not oxygen.

A basic full face mask can be obtained for $100-150, such as this one . Masks that are more full-featured will run in the $500-$1000 range.

You should be aware that one of the skills that you need to be able to perform to become a certified diver is to fully remove and replace your mask underwater. This skill requires you to be able to breathe comfortably only through the regulator in your mouth, since your nose will be exposed to the water. I think it would be better for you (and less expensive) if you were to train yourself to not inhale through your nose on scuba than to try to use a full face mask to compensate for this habit.

There is no reason that you can’t exhale through both your nose and mouth with a conventional mask either.