Sentence examples for but I kept from inspiring English sources

The phrase "but I kept" is correct and can be used in written English.
It is typically used to show a contrast or continuation of action in a sentence. Example: I was exhausted from hiking all day, but I kept pushing myself to reach the summit. As for your question about my worst experience during a vacation, I would have to say it was when I got food poisoning on the second day of my trip and spent the rest of the vacation bedridden in my hotel room. But I kept trying to make the most of it by ordering room service and watching movies.