Windows ties a specific ICC profile to a specific monitor, yes. I would recommend calibrating and using your photo editing monitor

What model monitor do you have? If it’s a low end panel, even if you have 100% sRGB gamut coverage, your calibration results may be disappointing. I had the exact same experience until I bought a Gigabyte M32U which cost me a pretty penny, but after calibration using the exact same methods I had always used before, it looks stunning.