Can symptoms of pregnancy occur from satrting a new birth control pill?

Possibly: According to roger harm md from mayo clinic, a progestin –only oral contraceptive may cause nausea, breast tenderness & irregularity of bleeding.

Yes : Depends on the pill and your sensitivity to the hormones. Some women are more sensitive to hormones in the pills than others. No hormonal contraception may be a better option for those women who can't tolerate hormonal contraception.