How do I fix a problem with the IRS stating that I do not qualify for stimulus because I was claimed by another person in 2018. I know this to be false.

While you may have filed your own taxes, that doesn't guarantee that another tax return wasn't also filed listing you as a dependent.  Unfortunately, there isn't a simple way to fix this and the IRS will not provide you with information about another taxpayer's return - even if it is a return on which you are listed as a dependent. 

You can file your 2019 tax return to see if this might qualify you for payment later this year, but there is no guarantee that it will work. 

Absent that, the last way to receive the payment will be to claim it on your 2020 tax return when you file in 2021.  If the IRS determines that you are not eligible for an advance payment there isn't an appeals process other than to claim the credit on your 2020 return.  

The fact that you did not indicate on your tax return that you could be claimed by someone else does not mean that no one else claimed you on their tax return. If the IRS records are accurate, some one else apparently claimed you in 2018. Were you eligible to be claimed by someone else such as a parent?

What is your filing status for 2019? Are you required to file a return and if so have you filed it? Did you claim yourself by leaving the box unchecked that someone else could claim you? If you are not required to file a return for 2019, did you use the non filer portal to register for the stimulus?

 https://www.irs.gov/coronavirus/non-filers-enter-payment-info-here