This summer I had a new blower put on our RUUD furnace and it worked great for the AC. Now I went to turn on the furnace and it clicks on at the thermostat and the igniter kicks on and the furnace is working but it doesn't blow out any heat. After the furnace stays on for a couple minutes it shuts off. Any help would be appreciated as it is getting cold in Ohio!

Start with the simple first. Check all flame sensors and probes.
My old oil furnace had a flame sensor that if it didn't detect a flame for about 45 seconds, it would shut the furnace down.

The furnace is wired to shut off soon if the blower doesn't come on.

Usually the furnace uses a separate winding in the blower motor to give a slower speed than the A/C. It is controlled by a separate relay. It sounds like whoever installed the blower failed to connect the heating cycle windings. My feelings is that they should return and finish the job they were already paid to do at their expense. They may not see it that way.

It is also possible the relay decided to confuse things by failing.

While waiting to call them in the morning, try turning the fan switch from auto to on. If the blower starts up, you can then turn on the heat, and it should work allowing you a cozy night's sleep.

If that doesn't work, it is likely the blower plugs into a circuit board. You could open up the furnace and see if you can locate the wires coming from the blower to the circuit board. You could try wiggling the plugs around hoping the problem is just a loose plug.