Firstly, remember to include the smaller details. Just a name, logo and livery design won't cut it. At the very, very least, you need a registration and flag, because without those, we have no idea where your airline is from. Also things like coloured door frames, specific aircraft name, aircraft model, belly text, that kind of thing.
Take inspiration from other liveries, both in real life and on AE. Don't directly copy what's been done before, but use those liveries as an inspiration to make your own idea.
For making shapes that aren't the traditional circle, square, etc., I'd recommend using the pen tool. It might take some time to get used to it, but once you know what you're doing, it becomes really easy, and it'll improve livery quality ten-fold versus just using the shape tool. If you need help or advice on how to use it, DM me, I'd be happy to help.
And finally, the most important point, not just for you, but for all new livery designers: Take your time. Don't just spend a few hours on a livery, get it done, say "ehh... Good enough", and upload it. Take days, if not weeks, to make, develop, refine and perfect your livery. Trust me, the reward will be immense. The best and most-loved brands you see here on AE are the results of many months of trial and error, development, failed concepts and refinement.
As before, DM me if you need any further advice or help. Hope this helps!