The engine suddenly started running rough, added fuel injector cleaner, ran that through for ~10 miles and then refilled tank with high octane fuel, still rough, exhaust smells strong like rotten egg, and the exhaust seems much hotter than normal. Also the check engine light is flashing, my code reader does not work on this vehicle so don't know what code it's indicating. Do you think it's an O2 sensor, MAP sensor or spark plugs? Car has over 200,000 miles ran fine until now.

Often times the lower octane fuels have some sedement that settles at the bottom of your tank. So when you run out the gas often times these sedenments work there way through the fuel system. Try and fill up with a high octane (91 or higher) and add a fuel conditioner and drive it. This will sometimes burn off the sedement and help to unclog injectors. If this doesn't work then you may need to replace your fuel filters because they may be clogged.

Put more than 3 gallons of gas in your tank- $20 = 3.5 gallons here. The bottle of cleaner specifies how many gallons of fuel is to be mixed with the cleaner. Usually 8-10 gallons for the small bottle cleaners. Whatever. Follow the directions. It will likely run like garbage for about a quarter tanks worth, but should clear up eventually, UNLESS - there was something wrong before you put the cleaner in. Have you put cleaner in before now? If not, why did you decide to do it now? If there was an issue before, that issue needs to be cleared up before trying additives, unless you are absolutey sure you have a dirty injector or two. Also might help to buy the highest octane rated gas you can for a tank or two. The more expensive brands (Shell, Exxon, Mobil, etc.) usually have some detergents in their gasolines that help clean injectors on their own too.

spark plugs injector cleaner have u been runing with low fuel pump may be on it way try fuel injector cleaner & fill tank 90 plus octane

Fill up your gas tank and ad a bottle of Lucas gas treatment/lube to the tank, be sure it's the treatment in a little clear bottle and not injector cleaner. After you've added the gas and treatment drive the car, with the head, driving lights, radio, heater, etc. all turned off. It may take ten miles or more but the check engine should go off and car will run normal. NOTE: Never jump start your car or use it to jump someone else's without referring to your owners Manuel.

I WOULD SAY YES BECAUSE THE LUCAS FUEL INJECTOR CLEANER IS JUST HELPING THE INJECTOR SPRAY BETTER

Replace your fuel pump. When you run a vehicle completely out of fuel, you will pull all the sediment off the bottom of the tank, and this will indeed clog fuel injectors, but first it will clog your fuel filter. After replacing your fuel filter, purchase a high-octane fuel injector cleaner, and add it to your fuel tank as specified on the side of the fuel injector cleaner bottle specifies.

remove dog house locate test port and install guage should be 45-60 psi

Even a small amount of bad gas can cause your problem.
So the first thing you need to do is remove your fuel tank so you can drain all of the old fuel out,then remove the fuel sending unit and fuel pump assembly thats in your fuel tank and clean the filter screen, after that you can reinstall the fuel tank,replace your fuel filter and I would have a fuel injector sevice done.
Unless you are very skilled in automotive repair, leave this one to a pro.

Try a fuel injector cleaner or higher octane fuel for a tank see if you notice a difference

very likely the fuel injectors are damaged, replace them, the fuel pressure regulator and all rubber fuel lines, also pull the gas tank and replace the short rubber hose at the electric fuel pump, I know this is expensive but even a few miles of running would have wrecked havoc on the rubber components, that rubber debris will flow through the fuel system and will plug the injector's, E85 melts it and skin for that matter.