Hey Lex!
I'm glad you posted here because this place is such a great support for people in your situation.
I understand where you are coming from. This is how I lived my life up until about 3 weeks ago. My teeth were in a bad way, I didn't have a lot of money and I had an intense feeling of shame and embarrassment about the state of my teeth. From my late teens and throughout my adulthood I've thought about how bad my teeth are every day.
About 8 months ago I decided I needed to take action because my teeth were making my depression and anxiety hopelessly worse - I could no longer live like this. I started posting here and researching how I could fund the treatment I needed and if there was a dentist out there that could help someone like me. I came up with a shortlist of dentists and slowly started to make contact with them. Firstly sending out emails and then working my way up to calling them. A few weeks ago I had my first appointment with a very kind dentist who helps people with dental phobia and is completely non-judgemental. On Wednesday, I'll be attending my 4th appointment. I couldn't even picture this happening at all only a month ago. The biggest regret I have now is that I didn't do it sooner and that I let my fear grow to a point that put me under so much unnecessary suffering.
Here's what helped me get to where I am now...
Posting here. Like you, I was so ashamed of my situation that I never told anyone about it. Having a place like this that I could come to and be understood and accepted did wonders to me actually taking this on. Getting many years of fears off my chest felt like a massive burden had been lifted off my shoulders. The success story section of the forum is a great motivator and I spent hours reading people's stories of how they overcame this and are on the path to something better. I started a journal as an outlet of my thoughts and concerns, as well as keeping track of my progress.
Googling dentists in your area that specifically deal with people who are nervous/embarrassed/anxious/fear judgement. If you google DENTIST *YOUR AREA* JUDGEMENT/ANXIOUS/NERVOUS/EMBARRASSED you'll get websites of dentists that mention the helping embarrassed (or whatever keyword you used) patients. From here, you can draw up a shortlist of dentists that you might like to see and get in contact with them. Check out their reviews on google/yelp etc and their facebook page if they have one. My dentist had fantastic reviews that mentioned how caring they were and their facebook page gave me an idea of what they were like also.
Once you've decided on a couple of possible candidates, break up contacting them into smaller pieces. I emailed them, which is great because it is largely anonymous and you can deal with the response in your own time. I simply wrote a short paragraph explaining my situation and how nervous I was and then ended with "can you help me?". It's likely that they'll invite you to call them to book in an appointment or give you a call. To help with calling them, I did some trial runs of phoning them after hours. I finally built up the courage to call them and began by saying I was interested in booking an appointment but I was extremely embarrassed and anxious. If the dentist is the right person for you, the dental receptionist will spend a little time reassuring you and asking you some questions. If they should care and understanding, you can simply say that you want to book in an appointment and that you want to only have a chat. I did this but ended up getting a comprehensive exam because the dentist was so nice!
Sorry for the long response. I hope something in there is of some help. Feel free to send me a message if you want to chat or bounce any ideas off.
Remember, you are NOT alone and you CAN do this!
Take care!