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I'm pretty new to German, and when I read and watched German content, I noticed that they sometimes use ich and mir in the same phrase. For example:
Ich war mir sicher, dass ich im Test die richtigen Antworten gab.
As I understand the sentence, in English I'd just say "I was sure,...".
I don't understand the function of mir.
Why is it there and what does it express?
German often uses a self reference to make statements that affect the subject itself indirectly sound more personal.
Ich kaufe mir ein Buch.
Ich hole mir ein Bier.
Ich bin mir sicher, dass... .
Technically, leaving out the "mir" leaves open the bit of information about whom you're buying a book for, whom you're getting a beer. Having the "mir" there, leaves no doubt about this AND it's super idiomatic. But it's not mandatory, neither grammatically (has nothing to do with transitive or not) nor semantically (English can convey the same message without the self reference), nor as a fixed expression that you can't alter. If you want to read more about self references and how they're used in German you can check out this article on my blog.
What you encountered is the reflexive expression "sich sicher sein", so it would be
Ich bin mir sicher.
Du bist dir sicher.
Er/sie/es ist sich sicher.
Wir sind uns sicher.
Ihr seid euch sicher.
Sie sind sich sicher.
The reflexive pronouns mir, dir, etc. have English correspondences myself, yourself etc., but very often an expression is reflexive in German but not in English. You just have to know that, and a good dictionary will tell you, so watch out for the sich.
In this particular case, it is not necessary to use sich sicher sein, as sicher sein has the same meaning. The Duden gives this example:
ich bin [mir] sicher, dass er noch kommt
The answer is indeed that it is an example of a reflexive verb, so mir here is somewhat like myself. Many German verbs are transitive (they require an object) and if there's no external object, then do it to yourself. ;)
Sometimes you can avoid these constructions and some people do. For example, in my opinion there seems to be a rise in saying "Ich erinnere das" ("I remember that") instead of "Ich erinnere mich an das" ("I remember that", but correctly).
(Sorry not a good answer, but I can't comment yet and wanted to say the next bit.)
In case of your example, you could one-up your game and get really existential by saying "Ich war mir meiner nicht sicher".
