I always thought platinum was a very stable metal and didn't react to other substances on the whole.
For some strange reason my finger has become discoloured underneath my platinum rings. I can think of nothing out of the ordinary I have handled today and I have never had a problem before.
sounds like you have had a little bit of oxidation occurring - quite rare actually as Pt is one of the most inert metals. Had your hands near any acids, even lemon juice (citric acid), as that can cause the oxidation process to PtO2 (known as "Adams catalyst").
Often colouring in gold is from the other chemicals in the alloy (lower K (caret) being higher risk)......your platinum bands aren't a PT alloy are they as that is an alternative....