How to check for short circuit in coil
Your copper wire, based on the measurements given, would have a theoretical resistance of:

$$R=\frac{25.4\mathrm{m}}{\pi \times (0.5\times1.25\times10^{-3}\mathrm{m})^2}\times1.7\times10^{-8} \Omega\cdot\mathrm{m} \approx 0.352\Omega$$

Measuring this resistance accurately may be difficult with the multimeter you have on hand and would have required measuring the resistance of the fresh wire before winding. If your multimeter is not accurately calibrated and/or is not accurate at this resistance, you can't use the theoretical calculation to 'see' a short inside your coil. If you can repeatably measure a value from the coil, you could unwind the whole coil and compare the loose wire resistance to the coil resistance, but that sounds difficult with your thermal compound.

If your are using this coil for fairly low voltage applications (&lt;60VDC) and don't need a lot of reliability out of it, you probably didn't scrape the enamel in two places such that a short inside the coil has formed. If you scraped the wire a lot or need to use it for a long time, you would probably want to make a new coil.

To answer your other questions: you probably won't see a fluctuation in resistance on the multimeter; that would require an intermittent short circuit, which is fairly unlikely and would be difficult to accurately detect. Unfortunately, there is not an obvious 'tell' that there is a short circuit in a coil like this.