The spelling of "am guest" may seem odd to some, as it is usually written as "I am a guest." However, this spelling can be explained through the use of IPA phonetic transcription. "Am" is pronounced as /æm/, which is a contraction of "I am." "Guest" is pronounced as /ɡɛst/, with a hard "g" sound and a short "e" sound. When spoken quickly, it may seem as though the two words blend together, leading to the unusual spelling of "am guest."
The phrase am guest does not have a specific etymology as it seems to be a combination of two separate words.
The word am is the first-person singular present indicative form of the verb to be used in English. It comes from the Old English verb eom, which derives from the Proto-Germanic *immi.
The word guestcomes from the Old English noun gæst, which also originates from the Proto-Germanic *gastiz.
When combined, am guest is a phrase that typically means I am a guest or I am being a guest. This is not a commonly used phrase in English, but its etymology consists of the separate origins of am and guest.