It depends on what you're doing. How much theory background do you have? I would get familiar with all your major and minor scales, it'll really help.
You spell chords with sharps or flats depending on the scale, and the letters of the scale ALWAYS go in order. So in A major, you would NOT have A B Db D E F# G# A. See how I skipped the letter C? We don't want to do that.
Now if you're talking about using chromaticism, or going to non-chord tones, or whatever else, what you say is true. You want to use flats going down, and sharps going up. HOWEVER, this is not the case with what I pointed out. Chord tones are different, and we'd want to revert back to our scales.
This isn't always the case, but it's where I'd start out if I were you so you can keep track of what you're doing. Later on, you might use the Db depending on what the other notes around it are doing.
Sure there are outlying examples of this that might be contradictory or confusing, but if you stick with this and practice that, the rest will begin to make more sense. My guess is you were viewing your music horizontally, but not vertically. Always watch to see what kind of harmony your melody is intertwined with to avoid clashes and such.
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I'm not a string player myself, but I would rather have the music sound more like I want it to than to fear slurring wrong. I'd write your slurs, and if they're wrong, hey, you get to learn how to do them better from feedback or critique.
The forum-god @chopin just made a video about slurs, you would probably find this useful. Especially check out the music by some dude named "Vince" on the video, he's my favorite.