You are just being a nervous noob.
I've had worse bottling issues before, once nearly using my autosiphon as a pump to move the beer.
It takes a lot more oxygen exposure of our beer to cause any damage, than what we do in the normal course of our brewing AND in most of the boneheaded mistakes we make(including using our autosiphon like a hand pump if it gets stuck...in a basic brewing podcast years ago, one of the big wigs,
John Palmer, or Chris Colby (the editor of BYO) said that the amount of oxygen to actually damage our beer, is actually far in excess of what we do in the normal course of brewing and even most of our accidents. And requires about the amount of oxygen that we could pump in by emptying one of our red oxygen bottles with an airstone into our bottling bucket....not the normal amount of motion we make if we are careful brewers.
Also the effects of oxydation are long term they affect the storage of beers...Unless you pumped an oxygen bottle into your finished beer, you will have consumed your two cases of beer long before any signs of oxydation would show up.
Before you get all "first time parent" on your beer and start to panic about every little thing, read this thread and see, that despite what bonehead things that we might do, it still come out as beer.
https://www.homebrewtalk.com/f39/wh...where-your-beer-still-turned-out-great-96780/