It's likely that what you're experiencing is rotator cuff pain. The rotator cuff is a band of small (and very vulnerable) muscles that facilitate the rotating movement of the shoulder, and holding a barbell behind your shoulders is a very easy way to put the rotator cuff into its end range of motion. Spike is on the same wavelength here, as an easy way to reduce the load on the cuff is to widen your grip - the closer your hands are to your shoulders, the more stress you place on the rotator cuff, likely worsening your symptoms.
It's important to be proactive, because unattended rotator cuff issues can become extremely serious, and require corrective surgery. Thankfully, if you catch it early, simple warmup exercises performed before squatting and benching can strengthen the muscles to the point of preventing injury. This slightly old school diagram illustrates the most effective exercises for targeting the rotator cuff, so regularly performing these with low levels of resistance should (hopefully) clear your shoulder pain right up.
If you choose to squat with a wider grip, just be careful that isn't too wide - you don't want the bar slipping down your shoulders and causing serious damage. If you think the trade-off between alleviating pain and risking the bar security is worthwhile than give it a go - but hopefully some consistent warm-up should solve everything!