can i walk into an apple store to get my screen fixed without booking an appointment?

Depending on your location your store will have different peak times. From experience i would always recommend trying to get to the store within the first 30 minutes of the store opening, to ensure you are at the front of the walk in queue to be seen by a technician or genius.

Alternatively, you can visit the apple support website at: Contact Apple Support to book your self a genius bar appointment, or by using the apple support app.

Before you arrive for your appointment if you could ensure your phone is backed up and you have Find my iPhone turned off, this will greatly speed up the process of getting your phone in for repair.

Depending on your location, you can try it, but they're usually booked pretty solid at the Genius Bar, so you may have to wait for some time - better idea is to walk in with an appointment.

What Apple device you have can make a difference. If you have a phone or iPad the repair may take less time that if you have a notebook or iMac with a broken screen.