I got my first flat a month ago and it was a snakebite flat. I got it by hitting a small bump on the road with low tire pressure.
Since then I keep getting flats after a few days of riding. Every time I switch the tube and it's always tiny holes. I checked for anything in the tire, the rim seems fine and I always ride with the tube completely inflated ever since.
This is my 3rd flat now. I even tried switching tube brands. I'm pretty sure I installed them correctly.
You have addressed the pinch flat problem by running higher pressure.
If you are getting repeated punctures, even with new tubes, there is probably something still in the tire that is causing the tiny holes.
Finding the offending object can be difficult. I was unfortunate enough to pick up a tiny piece of steel wire (possibly a bit of paper staple) in my rear tire recently that just protruded into the tube. I had to carefully inspect both the inside and outside of the tire to find it.