I don't think that listening to music (even for a long time) "overstimulates" your brain. Just think about amounts of external stumuli your brain processes every day and every second! Usually it redistributes its resources, "ignores" irrelevant information, sometimes suppresses intensive or repetitive signals, so there is no harm from music per se.
There may be negative effects with regards to your cognitive performance. If your work requires a lot of attention, listening to music may interfere with cognitive activities directed to your tasks. On the other hand, the results of different researches seem ambiguous. For example,
this research shows that an individual can respond differently to various kinds of music, and in some cases listening to music can improve the levels of attention and concentration. And the
other research showed that listening to music in general decreases the level of complex task performance. Also complex music helped to perform simple tasks. And, finally, these effects were related to preference for external stimulation: those people who are easily distracted, more sensitive to environment and tend to, for example, do some additional things while working (like checking their phones) performed better without any music. On the contrary, those who don't prefer external stimulation performed better when music was playing. So, this is up to you to decide whether listening to music is really effective to you.
Speaking of general brain damage, there is no consistent medical evidence that earphones can cause serious brain impairments. If there are impairments, they are usually related to very loud music and high levels of noise in general. And these impairments usually "start" from the structural changes in the ear (for example, damage of the hair cells), but not from some fundamental areas of the brain itself.
To sum up, I don't think that there are any reasons to worry about negative effects. However, if you really experience some negative symptoms like headaches, fatigue etc., it is better to assess whether listening to music is the primary cause.