It could have been a Squeeze bottle, or it could have just been a similar design. Art Deco bottles often looked very similar to each other. Paul's might have bottled its own line of sodas separate from Coca-Cola, or it might have used different bottles at different times. The reason I think it might not be a Squeeze bottle is that where yours has "Trade Mark Reg." all the Squeezes I can find have the town name. Though there could be different variations of Squeezes, too.
I don't know if you'll see it in the photo, but if you look closely you can see "Trade Mark / Reg" on it below Squeeze, and the last letter in both bottles is an E. I don't know what Paul has to do with it, but one day I'd love to find out. Everything about it screams my bottle.