You're fine. Google the pro's and con's of chaning the oil at 3K like it's recommended and you'll see. One con being how expensive it gets. All you're doing is greasing the palms of the oil execs by changing your oil that quickly. It's actually kinda amazing how much life you can get out of an oil change.
tell ya what i do ,drain the oil ,buy som cheap oil ,run it in the motor for 20 min,this pulls all the carbon off,get it outa there change the filters and put the new oil in ,been doing it for 30 years works like a charm.
i run full synthetic and change every 6000 miles with filter only changes at 3000 unless i get into deep water. everything i own has made it past 200,000 miles on this interval.
some may call it overbuilt. my right foot calls it future scrap.
my rides: '92 yj work in progress, '77 pontiac t/a (no its not cliche black), '87 chevy 3/4 ton on 1 ton running gear, '79 gs850 (daily driver), '78 gs1000 (when i get the need for speed)