Am I eligible for the stimulus check, and if so, why haven't I received it?

Assuming that you are a U.S. citizen or resident alien, then yes, you should be eligible for the stimulus check, or Economic Impact Payment, as it is officially called. You have filed your 2019 return and are not a dependent, and are well under the income limits necessary for the payment.

The IRS has a page called Get My Payment, where you enter your Social Security number, birthday, and address, and it will tell you the status of your payment. The tool may tell you that it has already been paid with details on where the money was sent, or it may tell you that it needs more information from you before a payment can be made.

If, for some reason, you end up ultimately not receiving the payment that you were eligible for, you will get a tax credit equal to the payment you should have gotten when you do your 2020 tax return next year (assuming you are still eligible in 2020).

It depends on whether they made the determination of your stimulus "check" (advance payment) eligibility and amount based on your 2018 tax year or 2019 tax year. If your 2019 tax return had not been processed at the time they made the determination, they would have used your 2018 tax year, and determined that you did not qualify. In that case, you would not receive the stimulus check, even if you later filed your 2019 tax return and you qualify under the 2019 tax year. See Question B9 here:

Q B9. If the IRS used my 2018 tax return and determined that I am not eligible for a payment, and I later file my 2019 tax return that changes my eligibility, will the IRS issue a payment in 2020 based on the 2019 tax return? (updated September 24, 2020)

A9. No. If the IRS determined that you were ineligible for a payment based on your 2018 tax return prior to your filing a 2019 return, the IRS will not issue you a payment in 2020. If you meet the eligibility requirements based on your tax information in 2020, you may claim a credit in 2021 when you file your 2020 federal income tax return.

It's unclear whether your 2019 tax filing in March 2020 would have made it in soon enough for them to have processed it before they made the determination on eligibility for the stimulus check.