You have two options for claiming asylum in Canada. One is to come to Canada on a TRV (tourist visa) and claim asylum once you arrive. As others have said, your chances of successfully obtaining a TRV are likely close to nil due to the UAE deportation and lack of ties to your home country (i.e. the country where you hold a passport). Having said that, you can certainly try. You will need to show proof of ties such as employment, property, assets. You'll also need to show that you have sufficient funds to pay for your trip to Canada. Lastly, you'll need to make sure you declare the UAE deportation in the application (otherwise Canada will make a finding of misrepresentation and ban you from Canada for 5 years).
The second option for claiming refugee status is to move out of your home country to another country (e.g. neighbouring country where you have ease of travel). Once you have moved to that other country, you would have to be officially recognized as a refugee by UNHCR. UNHCR would then determine where you are resettled - some small chance it might be Canada but a much higher chance it would be another country. You don't get to chose - UNHCR would chose for you.
These are your two options for the refugee route. No point talking to Amnesty International - they can't help you in this regard.