I'm no medical expert, but the first thing you should focus on is improving your general health first, both mentally and physically. These are the largest factors that affects your performance and the amount of time you can focus on specific tasks, so get plenty of rest, eat healthily and have some physical activity outside of sitting at your computer.
Outside of health, this sounds like it may be a mentality problem. Try approaching the game(s) with different goals in mind like "I want to improve" or "I am going to try to relax and not worry about losing/dying too often". Give yourself an explicit task to focus on and everytime you notice yourself deviating remind yourself what you aimed to do, The goal of this is to have something to work towards and training your mind, reducing the likelihood of getting flustered.
Finally, if this seems like a consistent and unsolvable issue where you cannot manage excessive stimulation you may want to get a medical opinion. It may not be anything, but it's better to err on the side of caution.