I was going to say something to this effect as well. It depends on who the wins and losses are against. If you lose 10 even games against different 1 dans, it would be hard to judge if that would make you a good/bad 10kyu, it would really only conclude you’re possibly not a 1 dan 
(or you’re a 1d having a bad run of games 
)
I think though if you’re consistently beating players below a certain ranking, say you nearly always beat 16+kyus, then it would seem reasonable to say you’re confidently at least a 15 kyu say.
There probably will always be players that are x+1,x+2… kyu that are on a win streak and pushed up to this rank, or …x-2,x-1 kyu players pushed down to it, so individual wins losses are trickier to interpret.
I think similar to what you mentioned
If the same seems to happen again, that you find yourself stabilizing around lets say 13-15 kyu, after a bunch of regular games, then it seems reasonable to pick 14kyu as your rank, and hence looking back conclude that you’ve improved (a good bit! - and also congrats on the wins! ).