As you know, screenshots can be captured pressing and holding both Power (side) and Home buttons.
From your question, it looks like your Power (side) button is stuck in "pressed" mode.
Try to turn your device off. Then try to move (press and release many times) your Power (side) button, and eventually gently clean it. Then turn your device back on and test it.
If nothing changes, have your iphone inspected at the nearest Apple Store or Authorized Service Provider:
Apple - Find Locations - Location Selector
Regards
Giulio