Is white, odorless discharge more common in early pregnancy or is it more common right before your period is about to start?

The discharge you described is not able to differentiate between period and pregnancy. If you had sex since your last period and miss your period by 4-5 days, do a home pregnancy test. . If the result is negative repeat the test 4-5 days later unless you get a period by then. Use first morning urine and follow the instructions carefully. Wish you good health! Get HPV vaccine.