When I have my acoustic guitar plugged into my amp it starts this loud feed back hum. I thought it was the guitar but then I realized that if I touch only the A string it would stop. Also if I de-tune the string sharp or flat it stops. And it is only the one string. Anyone have a suggestion?
That's completely normal. Acoustic instruments are, after all, built to transmit vibration energy away from the strings into the air so they can be heard; but this process is reversible so any good acoustic guitar will produce feedback when close to a loud amp over which it's amplified. As long as the feedback only happens via the strings, it's not that much of a problem, just be sure to damp any strings you're not playing at an instant with your fingers.
Still, this isn't nice and should be avoided. You can avoid it best by turning down the amp as much as you can afford. If you have a PA anyway, you don't really need loud amps on stage. Place the amp high and as close to your ear as possible, or use in-ear-monitoring, this allows keeping the stage volume so low that feedback shouldn't be an issue.
You can also tackle feedback on specific frequencies with a notch filter, that removes the most troublesome resonances without affecting the overall sound much. Good modern acoustic amps usually have notch filters built in. But this only gets you so far: when you've eliminated one feedbacking frequency, you'll quickly run into others when trying to increase volume further.
If the amp is generating audible noise even when the guitar is not being played, then the string is probably induced to vibrate by the sound box i.e. sympathetic vibration.
As @Tetsujin suggests, the mains hum may be amplified by the sound box and then the bridge vibrates, and then the string picks this up by direct contact with the bridge. Sitars leverage this phenomenon.
Normal electric guitar feedback also leverages this, but electrics are not designed to mechanically amplify sounds quite like acoustics are.
It may be possible to dampen the string above the nut etc. akin to a wolf-tone damper. You can probably test this by resting a finger on the string up near the machine. It may also be something else entirely, such as a lose kerf (which buzzes) or poorly glued paper label inside the guitar (which acts like a kazoo).
Any vibration can quickly amplify in the sound box and then transmit to the strings sympathetically.
Several solutions to acoustic guitar feedback through an amplifier.
Acoustic guitars sound best when playing through amplifiers designed specifically for the acoustic guitar. Electric guitar amps are not the best solution in my opinion for amplifying any acoustic instrument. Many acoustic guitar amplifiers have great EQ and sometimes feedback reduction circuitry built in.
Place the amplifier in front of you facing away from you and your guitar.
Use a 10 band eq pedal or one of the many acoustic guitar pedals that have not only eq but feedback reduction features a as well.
Use a sound hole plug in the acoustic guitar.