Energy drinks are not particularly good for you although it is not true that the directly cause problems with your brain.
However, they do contain very large amounts of caffeine. Drinking caffeine in excess can lead to jitteriness,mood problems, and trouble with sleep (all of which are, in a way, brain problems). If you are very fatigued and need the energy drinks to cope, then you need to think about fixing your lifestyle so that you are less fatigue (sleeping and exercising more, for example) rather than relying on energy drinks to keep you going.
The other major problem with energy drinks is that they contain large amounts of sugar. People who drink large amounts of sugary beverages are at higher risk of being overweight, of developing diabetes, and other related health problems. Cutting down on sugar intake is an important part of living a healthy lifestyle.
I would suggest that you go to see your primary care doctor
, particularly if fatigue is a big problem for you. They can help make sure there is no medical reason for you to be fatigued, and they can give you advice on how to change your lifestyle so that you rely less on energy drinks.