I used to have a neighbor that had horrible allergies and would mow and garden in a full white suit that included mask, goggles, and went over their shoes as well. Hopefully you don't get a rash or any other reactions so all you would need would be a mask.
I'd look for a pollen mask instead of a medical mask. There's some reusable ones available that you can wash and they look more like bandanas than masks.
Example at Walmart
Medical masks can be absorbent to prevent water droplets that may contain bacteria from getting past the mask. I can imagine how this could be bad for allergies as it might absorb and hold allergens in the mask.
As far as only wearing it outside I think that would be more appropriate than wearing it all the time. Most indoor locations are air conditioned/heated which means air passes through some kind of filter at least. You might look into regularly changing your filters at home or looking into a higher grade of filters if you're having problems inside your house as well.