You will need all of your information ready before obtaining authorization in any of these apps. Pilot name, phone number, certificate number, exact area to be flown, max altitude, and specific aircraft, etc...
I use Android and PC (no iOS devices). I have found that the LAANC procedure through AirMap is either very confusing or just doesn't work. It tells me that FAA authorization is available but then says it needs to be a manual FAA authorization. I know that is not the case because I checked the FAA LAANC list and the Class D airport I wanted to fly near was on the list for automatic approvals.
So I used Skyward and it worked fabulously well. There is quite a bit of initial set up to do with Skyward, including setting up your user/pilot profile, adding your drone(s), creating an operation, and then attaching at least one flight to that operation. If missing any mandatory information, it will not allow you to place the authorization request. When all the info is there, you just place the request . It can be done well in advance of your planned flight. The authorization comes back within seconds. You can print it and take it with you.
Note that if it as a NFZ, you still need to unlock the zone in DJG Go.