Make sure you have a lightweight bike, no heavier than it needs to be.
I use a CX carry for apartment staircases. If you like this carry, chose a bike with suitable cable routing. Cables underneath the top-tube can interfere. CX carry needs a man's style top-tube. Horizonal ones are easier to shoulder than modern-style, sloped (compact) ones. If you have a step-through woman's frame, I can see the need for a handle, but you have to support all the weight by hand. Can you use a sling between saddle and bars?
Never carry your bike transmission side towards you !.
Smaller wheels can make a bike more manageable. using MTB 26" rather than 700c can help in tight spots. 24" is a really useful size but sadly ignored. 20" BMX wheels are used on some
urban mini-bikes.
If metal pedals are hurting, fit some high grade plastic, eg BMX ones.