The reality is, almost everything at the dentist's office can be done painlessly. I've had root canals, extractions, fillings, crowns, cleanings, and probably a few more you've never heard of, and almost all of them with no pain at all. For most procedures, you will be made completely numb (well, the specific part of the mouth to be worked on will be) before any work is done at all. So as scary as the drill seems, you should never feel any pain at all during drilling. If you experience even the tiniest bit, the dentist will stop and make you number.
Cleaning doesn't hurt but it can be a little uncomfortable, to be honest. Most of the cleaning involves a trained hygienist using hand tools to clean and floss your teeth. Typically they'll also use polishing tool which is kind of like an electric toothbrush. This vibrates a lot but isn't a drill, and doesn't hurt. Cleaning is usually done without anesthetic, but if you're extra nervous there are things the dentist can give you to relax, including "laughing gas" (a low level of nitrous oxide that calms you down), conscious sedation or "twilight", or just some local anesthetic to numb up the area.
X-rays don't hurt a bit. You'll be asked to bite down on a big plastic "bit" that holds some x-ray film (or these days a digital x-ray receptor), and then a picture is taken. Some offices have a panoramic machine that takes one big wraparound x-ray. More commonly you'll need to hold the bit in different parts of your mouth to take six to twelve-ish pictures. If you have a bad gag reflex like me this can be uncomfortable, but doesn't hurt.
But the first step BEFORE all this is to have a consultation with the dentist. He will have a visual look around your mouth with his little mirror, and usually will want to get some x-rays. And then you will have a conversation about what work you need. That's usually enough for most people on their first visit, without anyone doing anything at all to their teeth. Cleanings and other procedures can be scheduled later.
You are right that we're only guessing when we say your teeth aren't that bad. Only the dentist can really tell you, and usually only with some x-rays to show the non-visible parts of your teeth. From my own personal experience and from hearing from a lot of other patients on this forum, it's not typical that a single broken tooth at your age is the sign of major trauma. (Although, I think everyone here has had that feeling of, "surely they'll need to pull all my teeth!"). It IS a sign that you need to have that tooth fixed up before it gets worse, and it's possible that you'll need some other work too. There's no possible way to tell from your short description, but let me tell you this: I went back to the dentist at 40, and I had entire molars that had broken down to the gumline, and had been breaking and crumbling for over ten years. I could run my tongue around my teeth and feel sharp, jagged bits and big gaps all over my mouth. I hadn't brushed my teeth regularly in 20 years. Now, my treatment plan isn't short, but my dentist has built up and fixed each broken tooth, and I have an almost complete, white smile now. (I lost one back molar that was too far gone.) Strangely, many of the teeth in my mouth are completely fine. Others on here have been in similar situations and come away with only a handful of cavities. Each mouth is different. So, I certainly don't KNOW what you'll find out, but I can tell you that at your age, and with just the one tooth broken, it's pretty darn likely that your teeth can be cleaned up. That one tooth might need some major work, or it might need extracting, but even so, there's so many options (crowns, bridges, implants, partial dentures or "flippers") for replacing a lost tooth that your dentist will be able to fix it one way or another.
The one thing that is known is that the longer you wait, the more work you'll need. You certainly don't need to be lectured to know that, but I wish I'd listened more to that voice of reason when I was younger. I could have saved myself a lot of time, money, and dental visits by just fixing my bum tooth when it broke, instead of waiting and worrying while my mouth got worse and worse.
The gum biting thing just sounds like a nervous habit (completely uneducated guess there...). I do really think you could benefit a lot from finding a counselor, therapist, or coach of some sort to talk about the fact that you feel crappy. We all go through low periods in our lives, and I sound like an old man saying this, but life's too short to spend a lot of time hating yourself. Talking about it with someone who's a good listener can really help you take control of all the bad thoughts and to start acting and feeling happy.
Sorry, a little preachy in this response, but I really care about you (because I've been where you are in my own life) and want you to know that it can get so much better.
Take care...
