When I put injector cleaner in it, it stops for that tank. Near the end of the next tank it will start up again. I did get a code reading that it was miss firing on #3 cylinder a couple of times. So do you think a pro should clean it or do you think it is a bad injector.
Based on the use of injector cleaner and the problem going away and then recurring... Compare #3 spark plug to a couple others. Easily could be that the cylinder has a problem that is causing the plug to foul...oil will bake onto the plug as will coolant. The injector cleaner could be enough to keep the plug relatively clean for a while.
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None of the following should have a reaction to the cleaner as you stated, except for a dirty injector. Just for general info.
If the plug has a light tan color to it...cylinder is burning properly. That would lead me more to an injector issue...wiring(abraded, ate by rodent, etc), broken or not fully plugged in connector, injector not sealed to fuel rail (failed o-ring), dirty injector. Debris getting to an injector is usually a failed filter or a sloppy mechanic that introduced it into the fuel system after the filter. It can also be the result of injector cleaner added to the gas tank and loosening debris in the gas lines after the fuel filter. A metal gas line that has been repaired with a rubber hose is subject to that hose rotting internally and flaking off debris.
Using a lot of safety gear and in a non-explosive, flame, or spark inducing area...Injectors can be cleaned off the engine...using 12 volts in a intermittent fashion...not a constant 12 volts. Injectors work by receiving very short pulses of electricity. A constant 12 volts will ruin it. Some tubing, a spray can of carburetor cleaner, and short connection of 12 volts to open the injector to allow the cleaner to pass through will quickly allow you to see if the electrical part of the injector is working, if so...watch the spray pattern of cleaner exiting the tip...should be a fine even strong mist. If not or dribbles, injector is dirty. Sometimes you can backflush them. Don't expect large debris, it only takes a very tiny particle to plug them.
A failing coil wouldn't be affected by the cleaner.
As a side note...With a 15 year old vehicle anything is possible...multiple problems are common. Very common are vacuum leaks...a smoke check is the easiest way to find leaking intake manifold gaskets (today's plastic manifolds are famous for warping and leaking), rotted hoses, cracked plastic connections, failed vacuum valves, etc.