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There are a non-zero number of places that will sharpen knives for free to get you into a store; that and a cheap honing rod will keep a knife alive for quite some time.
The thing your slicing sticking to the blade isn’t actually a sharpness issue, it’s blade finish. Shit sticks like all hell to shiny polished knife flats, but might come right off of something with a cloudy finish.
Ah, I have a few of those too. I’ve never let it get in the way of sharpening; the coating doesn’t seem any weaker at the newly ground edge ever. But in terms of food release, they definitely are slide-ier than polished steel, but they don’t like letting food pop off like a granton does.