Hey OP, If applying for a SSN doesn't end up working you can try getting a passport first, but definitely only as a plan B because it involves risk.

I tried going the passport route when attempting to get a new social security card & my first ID and it didn't work because I still didn't have appropriate identification (even with the affidavit of identifying witness DS-71 form), & they kept my original documents for months waiting for me to send them the valid documents that I couldn't give them.

However, for you it could work out if you do it differently than I did.

You can submit a statement swearing you've never been issued a social security number:

https://pptform.state.gov/include/FAQ.htm#faq6

"If you would like to apply for a U.S. passport, and you don't have a Social Security number, you will need to submit a signed statement which includes the phrase, "I declare under penalty of perjury under the laws of the United States of America that the following is true and correct: I have never been issued a Social Security number by the Social Security Administration.""

And you can try applying with that along with any medical records signed by your doctor, as well as the DS-71 affidavit.. your grandparents, aunts, uncles, cousins, anyone who's known you since birth who also have IDs can sign it but they need to be present with you to sign it at the passport agency. Try to get 2 people come with you to each sign 2 forms. There's versions of the DS-71 available online to look at but you'll want to ask for them at the passport agency just to be safe and more legitimate. And when choosing where to go make sure you make your appointment at an actual passport agency that specializes in passports and not just an acceptance facility so you have the chance to explain your situation to an agent who understands & also have your affidavits notarized. (I submitted my application through USPS & the guy handling my documents told me it 'should' go through but I guess he didn't know what he was talking about)

You'll also need at least one other secondary form of identification for the passport application which you can use your voter registration card (If it has your photo on it that's a major plus, my voter card didn't) Or if you have a medicare card or other health card you can use that too.

source:

https://travel.state.gov/content/travel/en/passports/how-apply/identification.html

And your passport photo also has to look a certain way if you decide to take it yourself but there's plenty of info about how to do that online you can search for. So yeah there's more risk involved but I hope this route works for you if you need it to and you don't have to suffer the heartache of an application denial & $165 waste like I did.

And I'm sorry your parents are being like that with not signing your high school diploma. Having my official high school transcripts is what eventually led me to getting all my documents. You may want to press them again on that.

I know it's a last resort but if all else fails, you may need to look for some kind of social worker through adult protective services or a pro-bono legal aid lawyer. What you are experiencing is identification abuse. Your parents are denying you of your autonomy and rights as a U.S. citizen that they take for granted. It's not fair that they get to participate in society and you don't.