Do you need a shuttle to get to southwest?

Yes

I believe you can go into the main airport and then take the tram to Terminal 3 from Terminal 1 otherwise you will need to get some kind of shuttle and I'm not sure if they have one that goes direct from the economy a lot to Terminal 3

Southwest Airlines flies out of Terminal 1. From the Economy lot, the shuttle will drop you by ground zero entrance to Terminal 1 at McCarran/Harry Reid airport. Once inside terminal 1. Its a short walk over to the entrance door from the drop off point. Once inside, there will be signs posted on where Southwest Airline ticket counters are for bag check in, boarding passes, etc. From there you'll go through TSA sec check and off to your departure gate. If you're arriving back to Terminal 1, go to the ground zero exit door by baggage claim, on the lower level of that terminal, and the economy lot Terminal 1 shuttle will pick you up and take you back to the parking lot. Look for the signs for the economy lot 1 shuttle pick up when you exit from the terminal 1 building. Just remember where you parked :)