I am just a bit taller than you so I will give you my 2 cents based on my experience.

Sizing is very confusing. Bikes fit differently. There are sizes and how the frame is measured which don't always match up. Then you add it compact geometry (sloping top tube) and it gets more confusing. Plus if you dont' really know what you like then all this becomes to theoretical.

The thing to do is go to a couple of shops and ride some bikes and figure out what size you want. You might still end up with 2 sizes. I would say you should go for a 56 (22 inches) and maybe a 54 if its a compact geometery but only you can decide.

Good luck sizing is really tough, but if you find the right fit its really great. You might not get it right the first time so don't overthink it too much. There is always another bike. Also you might consider buying a complete bike if this is your first road bike. Its tough to build up a bike and then it dosn't really fit. Its happened to me.