Are you on a septic system or a local sewage collection system? It also appears that you are collecting alot of surface water into you sewage system. Find the source where it is entering your sewage system. Surface drains and storm drains are to be seperate from sewer drains. Most municipalities prohibit storm drain ties into sewer drains; they don’t want to treat the extra water. You definitely do not want a surface drain or storm drain piped into a septic system.
If local codes permit you can install a BACKWATER VALVE Also called a check valve.
The problem with using these devices is in case the main sewer is over loaded and puts any pressure against the flapper of this back water valve water will NOT enter your home BUT you also will not be able to use any fixtures until the pressure is relieved.
If you do go for this installation place this BWV in front of your building house trap and have it accessible for inspection and maintenance when required.
There are other options available BUT this is the easiest and cheapest available and it works.