I am a big believer in Fray Check for exactly this type of situation. I am never with out a bottle in my machine table drawer. Sometimes you just have to fray check it , and move on.
Note a little bit goes a long way. Use the tip to apply only in the seam allowance area. Put a small amount on the edge, and wait for just a few seconds as it will "wick" just a bit, before adding any additional. Do not iron Fray check while wet. Put enough to "coat" just the seam allowance area to the stiching line, do not go over , past the allowance as fray check does tend to darken the fabric .