What could happen to my cells? I overcharged them a bit
The open-circuit output voltage of your Li-ion cells (what you have measured and reported) depends on the specific chemistry of your cells.  4.3V is not uncommon.
The main issue here is that you are not using an inexpensive charger that is specifically designed to properly charge your expensive cells.  I recommend such a charger.  A simple power supply with a 5V output is not suitable.
I believe that your cells will continue to serve you well once you invest in a proper charger.