Ok...I have and do have the same feelings you do. There are 2 types of schools: Those that have a true beginners curriculumn and those that do the standard cardio, show you a move...you drill it...show you another move...you drill it and then you roll.
Now, my problem with the 2nd one is that when you're older....me I'm 40...and out of shape...I'm 300 lbs. This gets VERY discouraging. You can't do a lot of the cardio without almost throwing up, you can't drill really well because of flexibility issues or not getting it because you are learning slower than the "kids" in your class. The oldest kid in my class is 24, another guy is 21 and the rest are teenagers. This is a new location...we're all white belts.
I would suggest that you might want to look at a school that has a beginner class. I am considering this myself. I know that at most gracie schools they drill non-stop. They drill, drill, drill, drill, drill until you get the techniques you are learning and you really avoid the drowing feeling, from what I see. I also suggest you talk to your coach after class and voice your concerns.
It's tough for us older guys to get in the mix...it really is. Many people tell us to stick it out but it's tough with wife, kids a job and being kind of out of the age bracket of the majority of the class. I mean I got kids older than the guys I am rolling with. I may take some private lessons or something to get myself caught up.
Now, if you stay where you're at...I would say that you want to drill as much as possible and go to open mats. The more you roll the better you get and if you get tapped just roll more. Also...don't "cock fight" on your knees, ask if you can work on your guard or top game. Eddie is right about that being a waste of time. What's really cool is if you are still spazzing the better guys will want to roll with you to work on their control techniques. This got me comfortable with the "closed space" of BJJ. I also drill against a wall and roll around in that space. I found myself getting real claustraphobic when I first got rolled up.
Sometimes you really are drowning and have to find the right spot for you. I take it you're not brazillian, so it's not a criminal offense to jump schools or find an environment that's more supportive for you in particular. I know I am considering going to my schools other location because it has more older guys there. I mean I'm old as my coach so me and him talking like homies and the kids are tripping. Don't get me wrong...my guys are great...but it still feels awkward.
Oh and for God's SAKE take it ez...pain management is VERY important. Every joint I had hurt...dang. Don't over do it. Oh and if you are a fatty like me...roll no more than 70% on your dudes. Other whites ain't used to the size difference...you don't want to accidentally hurt them or have them hurt you.