It can be a good idea to flush injectors to keep the tips clean and allow them a nice conical spray pattern for better fuel atomization and mixture in the cylinders .
This is critical for proper combustion process in the cylinders which will go to the catalytic convertors to be reduced into less harmful gases such as carbon dioxide and water.
Your system is running rich. Your oxygen sensor is reporting this to the computer.
Possible you have an air leak in the intake system that is allowing air into the engine without being measured by the airflow sensor which affect fuel injection. This is called a false air signal. You may have an intake gasket leak or air intake hose that is cracked. Maybe even a throttle body gasket that is leaking. Even a crack in the exhaust can cause this problem. Check these to make sure they are not leaking.
Finally, you may have a failing oxygen sensor above the catalytic convertor that cannot relate the correct information of the contents of oxygen in the exhaust to the computer. You can check this with a scanner that has the capability of using graphs to check the operation of the upper and lower oxygen sensors. If the upper sensor shows a flat line, then the sensor is probably bad and should be replaced.
The rear sensor is usually flat which is normal, reduced gasses at a normal level going out to the muffler.
An EGR valve you mentioned is only used to reduce combustion chamber temperature to prevent nitrate of oxygen ( NOx ) by redirecting exhaust gases back into the cylinder to lower temperatures. You may or may not have an EGR valve as modern engines using computers do not require the valves, unlike the old days of carbs and high emissions. Smog.
If you decide to replace the upper 02 sensor, use one from a dealer and not an aftermarket will-fit. They are a waste of money from the beginning and you eventually end up buying the correct one anyway.
Sorry for the long-winded lesson about fuel injection and emissions.