I accidentally inhaled weed smoke nasally and experienced burning sensation through my sinuses, now I have loss of smell and taste. Will it come back?

Yes. Yes, any changes to your senses that you feel you're experiencing after inhaling the smoke should return soon. It's likely that the inhalation caused your nose to become stuffed up, or that the smell of the smoke was so strong that it's dominating other smells and tastes for you right now.