If I was you, I wouldn't base what I think my spirit animal is off what someone else told me (Tibetan monk psychic or not!). A lot of people believe that your spirit animal will be an animal you connect closely with. Perhaps set aside some time to think about animals you connect closely to. Make a list of traits you have (and be honest) then see if it matches up with any specific animal.
Meditating on it is definitely a good way to go. It's been suggested that if you meditate with the intent to find your spirit animal before you go to sleep, it can encourage revealing dreams regarding your spirit animal. And as was said, you may find it through projection as well! If you see a reoccuring animal during any of this, I would look into it!
Here's some links: