Is my bike a good fit?
I think it's likely that the frame is just to large for you. A medium frame is generally too large for a person 5'4" (approx. 162cm) in height. 

What's going in is that distance from the saddle to the bars is likely too long, causing you to have to lean forward too much, which is causing your pelvis to rotate forwards also. 

When sitting on a bicycle saddle properly, the bones at bottom of your pelvis should be taking you weight on the wider, rearmost part of the saddle. There should not be pressure on the perineum or points further forward. When the pelvis rotates forward weight is transferred from the pelvis onto the perineum. Apart from being painful, that cuts off blood supply and pinches nerves which causes numbness.

The proper solution is to get a frame a size (or two, depending on your body proportions) smaller. A potential solution is a significantly shorter stem to pull the handlebars back and allow a more upright riding position.

You can try getting a bike store to try to fit the bike to you, including playing with stem length, but personally I'd look for a replacement bike in a smaller size. Try some different bike stores and see what recommendations you get for sizing and fit.

At least in most US states bicycles stores are considered essential businesses, and bicycle business is booming. You may easily be able to sell your current bike to offset the cost of a replacement.

Updates based on photo and info in comments:

As others have said saddle height is too high, your arms are straight in the first photo and your ankle is raised with the pedal at the bottom in the second. Elbows should have a bend and foot should be flat with a slight knee bend.

Given that, you actually look a quite cramped on the bike. Notice your back is straight and the angle between your arms and body is less than 90 degrees. Your knees look very close to the bars. I think the fore-aft saddle position is way too far forward, it should be set to get the pelvis in the right position relative to the feet NOT to adjust reach to the bars. Set the saddle height properly, then with a pedal straight forward your kneecap should be vertically above the pedal axle. 

I think excess saddle tilt may in fact be causing you to sit too far forward on it moving you pelvis bones off the wide part at the rear.

The whole bike does not look obviously big for you, so this looks salvageable. What I would do is sort out your saddle height position and tilt first, and get you sitting in it properly. Then figure out where a comfortable bar position is for you, then achieve that with a shorter stem and possibly shorter reach bars. You can also rotate the bars back a little to get a comfortable angle of the drops under your hands

It looks like you want to be in a less aggressive, more upright position so your bars will be approximately level with the saddle, which is totally fine. Once you are feeling more comfortable on the bike you can work on some back flexibility and lower the bars if you want.

You may want to enlist the help of a good local bike store to help you get set up right. You may not have to pay for a proper bike fit. A good store should help you get these basics sorted out if you buy a new stem and bars through them.

Here's a good video on basics of bike fit. Contrast your position on the bike to those shown in the video.