"Sprained" my big toe 2 months ago in soccer, and it instantly turned black and blue. Toe is still swollen and painful in spots. Is this normal?

No. No, not normal. Certainly consistent with a number of potential injuries to the toe. If you are still having trouble with it, I would consider being seen for an accurate diagnosis and treatment recommendations.
Turf toe. Very common to injure great toe in soccer or football. You need to give the area extra support by tapping it or using an ace wrap . Ice after playing , use iNsaids . Avoid going without shoes. It may not resolve until 6-8 weeks after your soccer season is complete.
Not normal. Bruising may be from a break in the bone or a torn joint capsule of the great toe. Have it at least x-rayed. An MRI may be required. Ice, rest anti -inflammatories until those studies are completed.