Where to start answering your questions?...
I guess the first thing is to say that I do yoga by myself and in a classroom setting -- both pretty regularly. When I first started doing yoga, I was amazed at what others could do & my competitive side wanted to push to "prove" I, too, could do it all right off the bat. What I learned pretty quickly, and what I think one of the biggest lessons I'm continuing to learn in yoga is that there is no competition among yogis. Finding inward focus and letting your mind go and grounding into yourself will allow you to go further. Patience with your body will allow you to gain a better practice. Taking baby steps and challenging yourself to find an edge but not "forcing" will allow you to go further, faster. The more you ground into your body and let outside distractions (like that kick-ass dancer right next to you in class who can bounce right into a handstand and hold it for 10 minutes without straining or the ticking of a clock or your grumbling stomach) the more you will feel the subtle changes that allow you to go a little further each time.
When I first started a regular practice a few years ago, I remember setting a goal: "By the end of this year, I will be able to get my heels to the ground in downdog." Okay, here we are a few years later, and my heels still don't reach the ground. It wasn't a realistic goal. Just because someone next to me has hamstrings that easily do this doesn't mean mine ever will. In turn, the person who has the perfect downdog may never be able to do full lotus and hold themselves up by their hands in that position as I'm often able to do. (Notice I said "often". Everyday in yoga is different.)
Okay, so all of that said. Is it easier to practice alone or in a classroom setting? I think this is really a personal distinction. I know some who can't "let go" in a class and move deeply in yoga. I know others, myself included, who thrive on the energy generated in a classroom and the guidance and structure and worry-free environment that a classroom provides. Still, sometimes, I end up doing a practice alone at home. Usually, when I do this, I end up doing what I have already conquered and know I enjoy. When I go to class, I get the challenge to do (or at least try or work toward) the things that may be, well, challenging.
Oh, and one last thought on class v. home practic, I learned a lot from doing DVDs. I sort of used them for a while to teach me a few things I wasn't understanding in a classroom setting. Then, I added a couple of workshops and individual lessons to get past troublesome spots that I knew would cause me injury or block me from moving forward. (Things like proper chatauranga so I don't hurt my shoulder rotators.)
And, yes, going to a class will help you learn to do poses correctly. Adjustments and subtle hints will get you to the point where you can really conquer the poses for yourself. You mentioned hurting yourself while going to a class. I've done that too. Again, having patience is really important. I have a very regular, intermediate-level yoga practice. But, I still have days when doing a full wheel or shoulderstand is beyond what my body can handle. While, the next day I may do the best of those poses I've ever done before.
And, finally, finding the right class and right teacher for you is really important. Time and again I've met people who were turned off to yoga because the teacher or the studio or the time of day wasn't right for them. I've had great teachers, okay teachers, and teachers that I would never grow with. Again, its about the inner self as much as the physical body. If you're emotionally or socially uncomfortable, its tough to turn out the exterior and focus on your own personal interior.
Okay, all of that said, I now challenge you to come to a yoga class with me. Odds are with your strength and your height, you'll be up in handstands before I am! Free Class November 3rd!.