I am a little confused, to say the least, but it looks promising. I understand that the formatting here is a journal-log sort of thing—meaning that there are previous entries, unless you start with 165 for some reason—but you can't just throw background out of the window. The thing to do here when making these kinds of things is to make a reference to something that happened in the past, giving a meaning and atmosphere to the entry. For this context, maybe you could mention near the start why the narrator randomly wakes up in a city? They treat it like a normal event, but they don't make any reference to it at all, which comes off as strange and confusing to me. Also keep in mind that someone with this kind of tone probably wouldn't keep amazing journals every single day or every time they wake up in some weird town, but they might consider writing with detail when it comes to significant events—especially if they're a relic-hunter that needs to keep tabs on relic-heavy spots. At the end, perhaps you could mention what the narrator's plans are for tomorrow (you could potentially give more information into the reason the narrator wakes up in random places and connect to the start), or if they'll be busy with some other activity that gives more information on what the narrator does.
I noticed that you had some grammar mistakes here and there, which I won't go into right now. The main thing that tripped me up regarding the writing was this:
The medieval guy and I with my buddy watched him spasm. He got up after that. He had a lady friend, who has this crazy British accent.
The first sentence: This does not flow/merge well with how the rest of the text was written. This kind of speech might go with some other dialect/form of speaking, but I think it would read better as "the medieval guy watched with my buddy and me", or
"my buddy and I watched with the medieval guy as the uniformed guy…", or some other variation of that. I seriously feel that the narrator would group themself with their friend, rather than with the medieval guy.
The second sentence, which messes up the next sentence: Who is he? The medieval guy or the white-uniformed guy?
Read over for places to put commas and dashes again, but that's mainly it. Hope you got the feedback you were looking for!