For my first medical exam I failed the dot test and had to take a test with a FAA agent looking at the control tower from about 1/4 mile. The white and green look similar but apparently I guessed correctly and passed. I need to retain the test document for each medical renewal.
On my last medical the doctor did not have a dot test but instead used colored strips of plastic that almost anybody could pass. So I suppose some doctors may be less concerned with this slight color blindness, it is really not a safety issue.
Shop around for a doc, or just take the lantern test and be done with it.