HI, thanks for using healthcare magic
The presence of white patches on the tonsils acutely usually indicates the presence of a bacterial infection.
The rapid strep test
may sometimes be falsely negative.
If you are not having any response to the antibiotics that you are using then it is possible that you are resistant to them and other antibiotics may be needed.There should have been at least a slight improvement of symptoms after 4 days.
You may need to revisit your doctor for another assessment.
I hope this helps