You mention that the latest puncture hit the part of the tube acing the rim, rather than the road. Earlier replies have addressed that issue and are spot on.
You mention a plague of punctures and I'm guessing that some may have been on the 'road'side of the tube. If so, here is some thought:
1. 110psi should be fine if it's within the recommended pressures for the tyre, as should your weight.
2. If you are patching the holes and the patches peel off, look at your patching technique or buy different patches.
3. If you are patching and the tyres puncture in the same place without the patch peeling off, you may not have removed from the tyre carcass whatever sharp object it was that caused the puncture in the first place. When you get a puncture caused by a sharp object, you really need to rummage around inside the tyre and ensure that you've removed the naughty item that poked in to cause the hole.
4. Tyre life. I hate to admit it, but tyres do have a shelf life. It will vary, depending on use, age and several other variables, but once cracks appear on the outside of the tyre you are approaching replacement time. Glass shards and stones can lodge in those little cracks and work their way through.
5. Some tyres resist punctures better than others. This is an area of fraught debate and deep loyalty, but as in most matters it is my opinion that counts. I run several road bikes (family of five) and all have Conti Gatorskins on the wheels, most pumped to 110psi. Problems are extremely rare. If grit and shards are starting to poke through cracks in your tyres, think about replacing them.
6. Fitting. It may be that you're pinching the inner tube between rim and tyre while fitting. This can cause punctures or simply weaken the tube and make a later puncture more likely. If you are like me, you'll never learn to get it right every time. Persevere and you will start to get it right more than you get it wrong.
Do not give up on running narrow tyres at 100+psi. The whole experience is improved by reduced rolling resistance. I hope this helps.