Hi pink kitty,
For me, when I was pumping as often as you, I would sterilise the pump just before I use it, then pump, store my milk, then wash with baby washing liquid then park it in the steriliser. When I need to use it again, I just press the button to sterilise. I dont't wipe it after I sterilise. Just take out from steriliser to use.
Impt to keep things as clean as you can as baby's tummy is sensitive when very young. Usually I pump and leave the washing to my hubby. Anyone at home to help you with the washing?
Day time then bo bian, I will have to pump and wash on my own.