Is this something common that I can tackle on my own? No matter if I push the signal thingy up or down it signals right. But if I don't lock it down just manually hold it down it will signal left.

I'm not sure if I should be tearing apart that part of the truck to see what is up with the switch because of the airbag.

 

That would most likely be the multifunction switch.
Tear the steering column apart and replace it.

 

Make sure you disconnect the battery and wait at least 2 minutes to completely disarm the airbag system before you start working on it