When I first put my car in gear it shakes really bad when my air conditioner or heater is on

With the vehicle off, investigate the center part of your A/C pulley (if you can get to it!)

See if it will turn with your fingers.

NOW!

Keep your fingers away!

When running, the pulley portion turns freely with the A/C off and any heat mode with defrost off (defrost settings turn on the A/C as to rid humidity from the air being blown on the windshield)

The pulley is turning free, driven by the belt. The center is not moving!

When you turn on the A/C or defrost modes, the A/C clutch (made in the pulley's center) which is an electromagnet, gets energized. In turn it "grabs" onto the pulley.

When it grabs on, the actual pump portion of the A/C unit starts to turn (This is the center you tried to turn with your fingers).

If it turns along with the pulley, the compressor is not "locked up" (ruined).

If the center remains still, with the A/C / defrost on, the A/C is locked up (ruined). More than likely the pulley is no longer spinning free because it is now coupled to the center which will not turn (as it should).

Your belt may be slipping and jumping on the pulley, this may also "drag" your engine speed down.

I am sure someone else may could have explained that easier.

The main thing is

No fingers near the running engine!

Moral of the story

Your A/C compressor may be locked up causing your problem.

Your turn,

The Medic