This is a frequent question that people ask at home, especially in those places where the sources of energy are not as efficient as they should be.

What you say in your question is correct only about the voltage, but you forgot to consider the role of the current. Once you apply any voltage to a resistor, a current flows through it. When you plug in your hairdryer, you are demanding more current to the main source apart from the one provided to the light; the source has a limited supply. Sometimes we just plug in so many devices, that our electrical system cannot drive them well.

There are devices called current regulators and they compensate for changes in the load. We call the load to any device that you plug in, like your hairdryer. Most electrical systems at home are designed with those regulators, but if you plug in several things at the same time, your demand of electricity might not be satisfied by the source, in spite of the regulator.

I hope it helps.