I hope I can help.

In British Columbia (BC) you need to be an official resident for a period of 90 days before you can apply for your health card. In the meantime, you can use a prescription your current prescriber provides you to bring to Canada. Another option is to have them write a prescription for a 3-6 month supply and purchase them in your country before. You would need a letter to transport them to Canada.

I would choose the last option.

Also, get yourself a family doctor as soon as possible. You need them to start the referral process for a psychiatrist.