and my fingers came away covered with blood

Use covered.

Your fingers could be covering (hiding) blood, but they will be covered with blood.

Use covered.

If anyone wants to know the reason for the blood, without clicking the link, it was a female goshawk defending her young.

"I touched my scalp, and my fingers came away covered with blood."

First, this is a Compound Sentence with two independent clauses connected by a conjunction "and."

I touched my scalp \ and \ my fingers came away covered\covering with blood

Since "touched" is Past Tense in the first clause, the other clause should be in the past tense too (it's a verb phrase with an interrupting adverb "away"): came away covered because...

If you use the Past Progressive "came covering" it would mean continuing action in the past, like in this sentence:

I opened the door, and she came running into the room.

The fingers touched the scalp. Blood got on them from a cut. As the person moved the hand away to look, the person saw the blood on the hand.