I urgently need to check these sentences for the last time. Thank you.

1) The doctor prescribed a nasal spray to be used (is TO USE a mistake??) three times a day.
Incorrect: The doctor prescribed me OR to me a nasal spray ...
2) Why don't you take SOME bicarb (or bicarbonate/a bicarbonate dose/sachet only for sugar?)
incorrect: A bicarbonate
3) The surgeon put my ankle in a cast.
(or put a cast on my ankle) Can you turn into the passive?

1. "to use" or "to be used" - either is fine.

"prescribed me" is incorrect, but you could say, "The doctor prescribed a nasal spray for me ... "

2. ... take some bicarb/bicarbonate/antacid
No need for "dose" and "sachet" is incorrect, yes. Packet would work, though, since that product comes in several forms: a tablet, a dissolving tablet, a chewable tablet, a packet, a spoonful (of the liquid form)

3. Yes, your alternatives are fine.