Choice of two problems:- 1 there is a wiring fault, 2 bad layout or decoupling causing high frequency oscillations. So if you have a scope put it on the output see if you can see any wave form with no input. If its oscillating then the wave form is normally huge like+- Vcc p-p. in this case the layout and or decoupling is wrong. Often touching a sensitive part of the circuit will change the frequency or stop it, use a screwdriver. If your wiring is rubbish you might have wired it up wrong and used positive feedback instead of negative. If you have no scope build a high frequency detector, .1Mf, one end as input other side going to a diode to earth, junction of diode going of to your DVM on DCV via a 10K other side of DVM going to earth. Polarity depends on which the diodes connected. To test probe use the input signal, should get a reading.
Measure the Vcc, disconnect the amp, Vcc should not change by more then a few volts.
I am dubious about your heat sink, a big one is 250mm X 250mm X 75 mm, CPU heat sinks tend to be a lot smaller (100mm square) but fan cooled.
Frank