I can't speak from the Norse Heathen view point of a fetch, but I can speak on it from a Traditional Witchcraft point of view - bare in mind that this is what my answer is going to be, you'll have to speak to a Norse Heathen about their Interpretation.
There are many ideas about what a Fetch is, some Witches believe that they are created creates like Servitors or Egregore, generally created by some similar Ritual, others believe they are more linked to you personally like a 'Soul Mate' that has waited for you to exist and they stay with you, for a long time - most of the time unnoticed until they need to be, or until the Witch in question finally notices them and accepts them into their life.
Other ideas surrounding Fetches are closer to Familiars, working spirits that serve/be served by the Witch, we also have the idea of a Fetch-Mate, which is a bit different - this is when the Fetch is a bit more than just a Spirit you work with, though I can't say much more on that subject because it is highly UPG and can become innapropriate.
Fetches come in different forms, some testimonies from other Witches state that they 'appear as a person, but during trance work etc we shift into beasts', others have more salacious testimonies.
Ultimately, they are similar to a Familiar, yet, again, every Witch has a different view on them.
My view on Fetches, they are personal, attached to you.
My view on Familiars, they find you or you find them and you create a working/familial bond with them.
Seeing your own fylgja (while awake) was thought to be bad luck, and an omen of illness or death. I personally think it is fine to see your fylgja when you are pathwalking or journeying, as that seems to be the most apt time to try and connect with your fylgja.Freya Aswynn writes some more about it, I think. You might check into other sources.
As for finding which fylgja is yours, and what shape it takes? I agree with what Weather posted, which is essentially that they either come to you or you will find them. I think trancework and projection methods may be a better state of mind for you to explore determining what your fylgja most likely is. In my own experiences, seeing it in a dream, a visualize, or having some intuitive gut feeling about it isn't completely uncommon.
You should explore the topic yourself and see what comes of it.