You need to edit the strings.txt file to add your ship type.
The section below from the strings file is where the ship type is created in game. You can see the section "|Advanced Battle|Advanced Battle Raider". The left side is what the game reads from the shiplist. It's limited to 15 spaces maximum (that's total spaces not characters). That's why it only says "Advanced Battle". That's 15 spaces. The right side is what it says in game when it sees "Advanced Battle" in the shiplist. It says "Advanced Battle Raider".
|Advanced Light |Advanced Light Raider
|Advanced Heavy |Advanced Heavy Raider
|Advanced Battle|Advanced Battle Raider
|Raider-X Cruise|Raider-X Cruiser
|Adv. Salvage Cr|Advanced Salvage Cruiser
|Adv. Slaver|Advanced Slaver
To this section I would add "|Adv Battle Frig|Advanced Battle Frigate" Like I've done below.
|Advanced Light |Advanced Light Raider
|Advanced Heavy |Advanced Heavy Raider
|Advanced Battle|Advanced Battle Raider
|Raider-X Cruise|Raider-X Cruiser
|Adv. Salvage Cr|Advanced Salvage Cruiser
|Adv. Slaver|Advanced Slaver
|Adv Battle Frig|Advanced Battle Frigate
In the shiplist, where I'm assuming you have Advanced Battle Frigate written, change it to "Adv Battle Frig" (without the ""). This will make "Advanced Battle frigate show up in game.
There are a number of things in the shiplist that can prevent a ship from showing in campaigns. There's no easy way for me to know (or guess) which parameter(s) might be preventing yours from showing up.
The best suggestion that I can make is to copy (Ctrl+c) and paste (Ctrl+v) a ship that shows up in campaign and edit the specs to create your new vessels. Do this manually by opening the shiplist and copying and pasting. I don't recommend using shipedit to create all new ships. You can usually use shipedit safely to edit specs though after you've done the copy/paste. Some people won't even do that with shipedit. They prefer doing all editing with excel.
Only change the attributes that you need to. Don't change things like Years of availability or special role, etc.. Just change the power, weapons, and those types of things. The other attributes are some of the things that determines availability.
hope this helps