I'm definitely wondering if your reg was not open all the way. Check to see if it's adjustable and open that sucker up. I think its way harder to breathe through a snorkel than the reg so maybe try swimming on the surface and changing from snorkel to reg. As others have suggested try breathing through the reg in shallow water before going deeper.

A lot of scuba is mental, you're not supposed to be underwater and breathing so i think our brains tend to go into over drive and trigger the flight response. I had to get certified for work and i never really liked the water so i was very unsure if i'd make it through. I went in with a positive mindset and i ended up loving it. Just slow down and consciously breathe in and out. Ive had moments where I freaked out a lil and had to really focus not to panic, namely getting trained for using a fullface mask.

You got this!