It does sound like it's an issue with handling the colour profile you've got set up for your monitor. As a test, you could save a picture from a colour-managed program (such as Lightroom) as sRGB, which will embed an ICC profile into the file, and save another copy from a non-colour-managed program (for example IrfanView), which won't...
If the image without the embedded profile looks ok in the browser and the image with the profile looks wonky, I'd guess the browser is failing to handle your default monitor profile.
Do you have a "wide-gamut" monitor? For one of my monitors I have to add an extra config setting to Firefox (gxf.color_management.enablev4=true) otherwise it will mangle my photos that have embedded profiles. Apparently this allows Firefox to handle v4 ICC profiles instead of just v2. Sadly enabling that setting causes a bug that's been in there for years which stops it from displaying PNG files, but that's another story..!
I've noticed that the latest version of Chrome is also wrecking my images (they were fine in earlier versions), so it could be the same issue there.