Everything you have said in this thread so far == successful attitude.
From one newb to another, one minor suggestion for sanity purposes: try not to think about how you're doing in terms of how many times you got submitted. I know it's hard not to, but the truth is that pretty much any blue can submit either one of us an arbitrary number of times in a round. No blue is likely try to tap you 10x in one round, but if one decided to they probably could. So for us newbs, whether we are tapping zero times or 4 times in a round is for the time being more about your training partners than your progress. In other words, if you go to class and it happens to be all high blues and you one night, don't go home bummed because it was a tap fest. It's normal.
Instead, try to think about how you're doing in terms of defending things you didn't defend last time. If your experience is anything like mine, you'll find that if you stop to ask your training partners how to defend an attack after you get submitted by it, you will very quickly learn to defend much better, and that is a positive feeling of progress. As a medium-term goal, try to focus on picking up a couple of basic offensive position techniques - stacking guard pass, scissor sweep, hip bump, stuff like that. Those will take a little more patience but I have only been training for a month and am starting to hit the occasional scissor sweep against other low whites now so you won't have to wait too long.
Good luck & keep having fun.