Why is my sound not working and letting me adjust my volume?

First I would try as Talon has suggested, namely try installing the original screen to see if the problem persists.

The iPhone 7 series of devices have proven to be very unreliable, suffering from flex-based issues similar to the iPhone 6 Plus (Touch Disease). On the iPhone 7, the fault line runs along the top of the SIM card reader and affects the Baseband CPU and Audio IC. Any short copper traces running perpendicular to the fault line while connecting to micro-BGA pads, is subject to failing.

This can happen seemingly out of nowhere and usually follows a reboot of an affected device, like when you shut it down to repair it. Once rebooted, the phone exhibits symptoms that were never present before.

On the Audio IC, this particularly affects the C12 pad/trace although there are 4 pads/traces along the fault line. Of those four, the C12 pad (I2S_AP_TO_CODEC_MCLK) is the most critical as it is a communication protocol line between the CPU and the Audio IC. ''''

Here are the typical symptoms, as collated by the repair community:

1. Voice Memos app / Loudspeaker on call - greyed out
2. Siri doesn’t hear you / Caller can’t hear you
3. Most other Audio related issues that aren’t solved by modular replacements
4. Long boot times (3-5 minutes)
5. iTunes detects the phone but stuck on the Apple Logo

This is a repairable problem but it requires a micro-soldering repair. Although it can be a routine repair for an experienced tech, it can go sideways very quickly as the Audio IC is directly opposite the underfilled Baseband CPU.  An unqualified tech can apply too much heat and cause massive problems. So do your due diligence.