Cool! And a lotta fun once you got past the fear, right!?
The statistic is the average first time Trap shooter hits 13 birds. Now, personally, I don't buy that -- it's too high IMO. But that stat. Accordingly you did very well indeed.
I'd guess you are pretty young and were hitting the birds almost as soon as they came out of the trap house compared to others. I'd also say there is a good chance your 870 jammed at some point and you had to force it open or something. Do I have those right?
In any case, fact is, you did well enough that I would encourage you to continue developing your participation in that shooting sport some. The recommendation to get/use a longer barrel is a seriously valid one but don't get carried away too quickly in this which is very easy. Less is more for a while... Except the barrel.