Edith,
Is that your name? Welcome to the better 2/3rd's of the world, that being the part underwater!
I am also new to the board, but by no means new to diving. I do not agree with instructor's telling OW students on their 1st couple trys that "Perhaps this is not the sport for you". I have witnessed instructors telling OW students this before, their 1st day in the water, and a dear friend of mine who learned how to dive was once told this by her instructor, after suffering several panic issues & having trouble clearing her mask, and it drove her to tears as well. (May I add, she is now a very happy, apt & active diver).
Many years ago, when I learned to dive, OW classes were conducted at a slower pace, it took several weeks of classroom work & confined water & open water training to get your OW certification. Still, at that significantly slower rate, I was not a real natural, and struggled with panic & so forth. Granted, not as severe as yours initially, it took me many dives to ensure that I could get through a whole dive completely relaxed. The one thing I could say, however, is that I was able to realize when I would begin a panic cycle, and I would remember to stop for a moment, relax, and breathe until the panic subsided. I'm sure you know this now, but never consider breaking to the surface as an option when paniced!
Considering my experience learning, it still boggles my mind that any instructor would dismiss, or give up on a diver that cannot take to breathing underwater, or a whole new set of skills, or underwater sign language at the break neck speed that PADI anticipates the nowadays open water student to respond to.
Large classes & tight time frames can make the instructor a bit frustrated when a slower learning diver seems to be "holding up the whole class" & in turn, makes the slower learning diver feel even more nervous, panicky, etc.
It was nice for this instructor, to offer some private time with you to catch you up with the class, and obviously you responded well to 1 on 1 instruction, as you got through your module 1 skills. I think that private instruction may be the way to go for you.
Despite my panicky issues while taking my OW class, I was going to dive come hell or high water. You sound like you have the same resolve, good for you! You mention you feel that the panic is coming from your mind, & you feel confident that you can learn to control that. You can. Some of it however, is a result of some uncertainty & lack of experience or the fact that you have yet to perfect techniques such as clearing your mask. Practice, practice, practice. And if you can, better to do it in the safety of confined water (pool).
Years later, I am now a PADI divemaster, and I have been diving many, many, wonderful places & countries throughout the world. The journey has been incredible, and if you continue to pursue this wonderful sport, trust me it may very well change the course of your life as it did mine! I think you can get through this, you've got the right attitude, and you want it bad, & I think for the right reasons! Keep up the practice, the chin, & good luck!