I have a stress fracture in 3rd metatarsal of left foot. can i drive if i feel no pain? (my physio said it's fine) can it heal in 3 weeks?

Yes: And it's possible to heal in that time. The question of concern why did it happen? Have your vitamin d levels checked...

Foot orthoses: When a metatarsal becomes overloaded if will begin a slow fracture process. Custom foot orthoses are valuable in relieving the abnormal stress being placed on the metatararsal. Rest is also helpful.

Stress fracture: Bone typically takes 6weeks to heal and i would have you in a surgical shoe which would not be safe driving. Just because you have no pain doesn't mean the bone is healed. You can delay healing by driving etc..