I doubt if the flushing caused any damage.
Let’s start with the oil change. You say you took it to a &#$* fast oil change joint??? That was your second mistake. The first mistake was not opening the owner’s manual and following the instructions there about when and what maintenance your car needs.
Those fast oil change places off cheap maintenance because they hire cheap - unskilled employees and then push them to get more work done in less time, just begging to have problems. Find a local independent (not a chain or a dealer (dealers usually do a good job, they just charge too much.)
I can't tell you what condition the engine is in now, you should take it to that independent shop (Ask your friends and neighbors for someone they trust) and have them check it out. See what really needs service and what the current problems may be.
Chances are the best bet from the stand point of your cost of car ownership is to fix or service as it should have been. You will know more after you have a real mechanic, not a oil change kid has had a chance to evaluate it in person. I suspect you will be best off having any needed repairs done and from then on make sure you keep up with all maintenance. The most expensive maintenance is that maintenance that is not done or done too late.
Good Luck