I sold my old home on 3-7-2020 and realized a gain, so I used the exemption on this year’s return. I have currently lived in my new home for more than two years, but I should not be able to claim the exemption
No, you will not qualify for any exemption if you sell your current home "BEFORE" 3/7/2022.
Per Eligibility Step 4 - Look Back in IRS Publication 523, page 4, you do not qualify.
However, it's perfectly possible you may qualify for a partial exclusion if you meet the partial exclusion requirements also detailed in IRS Pub 527.
