quick answer is your gun is fine. I shoot surplus out of my mosin nagants regularly and only clean them every few weeks, I have no rust in my rifles, the rust takes a while to form, one week especially when it was already cleaned out fairly well is not enough to rust a barrel to the point that it's unsafe to shoot. maybe if you fired those 20 rounds and left it in a dank basement for a year it might but not after a week with a field cleaning applied.
ignore my complete lack of capitalization. I still have no problem correcting your grammar.
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