According to Dunning Kruger that's rather a good thing 😉
I've been programming for more than 30 years and I still feeling this impostor syndrome sometimes.
But let me tell you:
- This doubt is what will make you better (it's a powerful reason to improve)
- Every time you doubt, remember every past little victory and dare
- And YES! you're a real programmer! (as long as you commit to be)