Learn German: Komm sofort rein! - Come inside immediately!

rein is the short, colloquial version of herein (coming inside, toward the speaker) or hinein (going inside, away from the speaker). In everyday spoken German, people usually drop the he- or hi- and just use rein for both directions.

Is rein just a standalone word here, or is it part of a verb?

It acts as the separable prefix of the verb reinkommen (to come inside). Because this sentence is a command, the conjugated part of the verb (Komm) goes at the front, and the separable prefix (rein) is kicked to the very end of the sentence.

Could I say Komm sofort herein! instead?

Yes! Since the speaker is asking someone to come toward them into a space, the strictly grammatical word is herein. Saying Komm sofort herein! is perfectly correct, but it sounds a bit more formal or dramatic than the everyday rein.

Why is the verb just Komm without an ending or a pronoun?