I think you are confused by the jargon and names of the various types of microphones. No shotgun microphone will record audio from all directions, as you say 360° audio. They are specifically designed to pick up sound from one direction only and reject sound from all other directions, and generally, the longer the microphone, the narrower the pickup pattern.
What you may want to get, and I don't recommend this option, is a bi-directional microphone, one that rejects sounds from the side, but picks up sound from the front and the back.
When you mention the sound sounding muffled when you are behind the camera, this is due to the sound from the back of the microphone being rejected, not caused by the camera blocking the sound. You can test this by having a friend talk to you while holding the camera and raising it to shooting position while talking. You will keep hearing the voice just as clear when the camera is between you and the person's mouth as when it is not in the way.
One of the two options that I recommend would be a separate microphone for you going to either the left or right channel of the stereo audio tracks, and the shotgun microphone into the other channel. You do want a shotgun microphone, especially in a noisy environment, to diminish sounds not related to what you are shooting.
The other option I would recommend is one someone else also recommended, and the separate microphone going to another recording device, and later either marrying back to the video in a video editing app, or that separate recording be your script, and re-record your audio in a quiet environment for the clearest audio result.
I would strongly discourage anyone opting for an omni-directional microphone, one that records in all directions, because all those other sounds will likely drown our the sound you are trying to record. There are times you may want an omni-directional microphone, but that should not be a first choice in most cases.