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How are your measuring skills? Check the relief on your strings. That is how far the bottom of your string is from the 12th fret. This is the easiest fastest thing to check to diagnose your issue. I like my strings a little high but most prefer low as it is easier in the beginning. 5/64ths of an inch is a common happy place.
There is probably both going on but no need to make your playing experience more difficult than it need be.
Should it be a technique problem continue on with the lessons. You will resolve the issue as you build strength and kinesthetic awareness. One of the tricks I benefited early on from was figuring out which strings my bar finger was actually covering. By doing this I could press harder when needed rather than pressing everything too hard which made me tired and sore.