Eyeglass Loop Paradox

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(Fictional) As a time travelling historian I was sent back in time to the medieval times by my department of research based at Oxford University. I came across a couple of estranged villagers who were bedazelled by the fact that I had came from nowhere with a bright light surrounding me. The villagers thought I was an angel and other villagers, once this spread around thought I was a person who practised the dark arts, obviously I was set for being burned, however these circumstances were anticipated by Oxford and they gave me a laser cutting device proir to going back in time, as of this I was able to escape the dungeon of the castle I was imprisoned in. My luck ran out though as I was faced with a huge locked gate with no way through, suddenly I heard a voice from outside the dungeon barred window; it was me! Myself passed me a key to open the door, I unlocked it and carried on carefree but was eventually chased by the guardsmen, my time device began fluctuating for some reason and I was sent back in time about 3 minutes ago, there were no guards around anymore. I noticed I was outside the dungeon barred window and saw myself stuck at the gate like I was, so I shouted to myself and gave myself the key I had been given. Afterwards another me showed up, ran his hand over the key and a number appeared-1725, the future me then left after saying thanks, I then escaped and went back to the future. Here is the paradox, if i was given a key to open the door and I gave the key away also, that would mean that that loop would carry on, but for how long? Three years later I decided to go back to the moment I was outside the castle and perfrom a carbon dating analysis, I read the number, it said 1728 years. I said thanks to my past self and returned to the future. I have a solution to this paradox, (which isn't really a paradox in my opinion), but I would like to know any solutions and ideas of the concepts put forward in this paradox that anyone has to offer. I will explain the solution soon after I have had a few replies.