I have VOX VT100X that comes with a AUX input, usually used to play for example a backing track via a phone. Can i connect my PC to the amp to play music via said AUX input or will that blow my amp?
Use the headphone out from the PC, and carefully raise the volume on both PC and amp. Works for me. Connects are screened cable. You could also plug straight in where the guitar jack goes, but you probably want to have guitar in that socket. Due to guitar amps being somewhat biased tonally, the sound won't be fantastic, but it'll be pretty good.
The manual available online for the VOX VT100X is strangely reticent about the type of jack provided as Aux In. But by comparing the graphic representations for Aux In, Headphones, Main Input and Foot Switch we can deduce the first two are mini-jacks, the latter two are 1/4" jacks. As the obvious source for Aux In these days will be a phone or tablet's Headphones output, I think we can also assume it is designed for a stereo signal on a TRS mini-jack plug. And this is also what your computer's Headphone Out supplies.
The level will be in the right ballpark. As always, start with all knobs turned low, bring them up as required. It is possible you'll get a nasty, abrasive hum, particularly if the computer is being run from mains power rather than battery. In this case, you'll need to investigate getting an isolating transformer.