Should I be calling a plumber or someone from my water supply company to test for contaminents in my water?
If you are on a public water supply, there may be water test results already published on a quarterly basis.

If you are doing your own testing, generally an environmental testing company or consultant (rather than a plumber) - in many cases you can save money if you can follow directions carefully and take the samples yourself, for testing at their laboratory, rather than having a consultant come and take the samples for you.

If it's ONLY the one bathroom, it's more likely something in your pipes than in the general water supply.