I am 3 days late on my period and experiencing pregnancy symptoms but the test is negative. is that normal?

True "pregnancy" symptoms would occur when the hormones that turn a test positive are circulating in the blood at high enough levels to turn a test positive. A negative test implies no pregnancy or too early to have the hormones. The symptoms may be unrelated. Some normally regular women occasionally skip a cycle or two. You can always retest at any time.