Happy Christmas friends. I am looking for a simple translation of the word "redeemed". The context is that I am redeemed by Christ. Any help would be appreciated. Thank you!

There are often things one can say succinctly in English (or any language) which may take more words in another language, and short literal translations may not always be possible, especially for a past participle like "redeemed". There's some ambiguity in the English slogan "Redeemed", but people are generally going to know you mean it in the Christian sense. That may not be true in Gaelic.

First off, there are several verbs in Gaelic which could be used for the verb "redeem" in the context you want. Christ is often referred to as the slànaighear, which can be translated as "savior", but is also translated as "redeemer". Using the root verb in that term, slàn, "Slànachadh mi" means "I was saved" or "I was redeemed". However, there's another verb, saor, meaning to "free" someone or something, which I believe is more commonly used nowadays by Christians in Scotland when the religious meaning is intended, as in "Saoradh mi", meaning "I was freed" or "I was redeemed" [from sin, in the religious context].

There are two other verbs which can be used in the same way: "Sgaoileadh mi" and "Fuasgladh mi" can, in the right context, be understood as meaning "I was freed" or "I was unbound", and I think each of them was sometimes used religiously in the past, but they aren't generally used that way now in Scottish Gaelic, so far as I know, so I think we can skip over them.

That leaves slàn and saor. Both have other meanings as well. The verb slàn can mean to "heal" or "cure", and saor can mean to "free" someone in just the general (non-religious) sense. Also, slànachadh and saoradh are not really past participles, as "redeemed" is in English. They are what are sometimes called "impersonal verb forms" using what are called "verbal nouns", and without boring you with the grammar, let's just say that in order to make sense, they are usually coupled with a noun or pronoun, like the mi ("I") in the examples given above. They can also be used as adjectives, but once again normally with a noun which is being modified.

So, technically, I think the closest to what you want is a two-word expression, either "Slànachadh mi" or "Saoradh mi". With the first one you run the risk of the expressions being misunderstood as "I was healed", and with the second one there's the possibility of someone thinking that you just got out of jail ("I was freed"), but I suspect that a Gaelic speaker will understand that you mean saoradh in the Christian sense. All that being said, the impersonal forms are used much less now in Gaelic than in Irish (where they are very much still alive), so if you were to use just "Slànachadh" or "Saoradh", especially if it's capitalized, I think a Gaelic speaker would get the point, especially with Saoradh.

If you want to be absolutely clear, you could add a bit more:
'se Crìosd mo Shlànaighear
"Christ is my [Savior/Redeemer]"

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I'm not a native (or entirely fluent) speaker, so be sure to wait for confirmations/corrections, especially for tattoos.