1987 Honda Accord Engine Dying after 10 minutes

A couple months ago I went and filled my car up after I was just about completely out of gas. Since then my car is constantly dying. When it sits over night the car will drive for about 10 minutes in the morning before it starts dying. Whenever I slow down at a light the car dies, or it dies when I'm going around a slow corner in a city. Almost anytime I'm going really slow it'll die, I have to keep some pressure on the gas pedal at all times to keep it from dying. When it doesn't die it often revs itself up and down like someone is pressing, releasing, pressing, releasing the gas pedal over and over again. A friend thats a small engine mechanic suggested to try Heet and I've went through 2 more complete tanks of gas, one thing of heet each time I filled it up and it hasn't helped at all. I don't know if it water in the line somewhere, or if I'm completely on the wrong trail. The car always starts back up btw.

Thanks in advance for any help! Greatly appreciated!