Dude, go back to the gym! You just went too hard. Next time you will know better how far you can push yourself. Of course the experience was embarrassing, but it's also not the end of world. I think most people understand that when you go beyond your limits sometimes you get sick.

Don't let this ruin the progress you have made and the discipline you have shown! What's the worst thing that can happen when you go back there? They won't kick you out. You apologized and as I said, people at gyms are empathic towards these types of ordeals. What else could happen? Some funny looks? A joke maybe? Who cares man. Turn up the music and think "fuck em" or just laugh it off. Because really my friend. This is not as big of a deal as you think it is!!!

Keep going strong!