I would suggest popping out the memory card and reseating it. I'm guessing you may have already done this. I'd try another memory card (if you have access to one) just so you can say you did. It is possible the volume key is rests in is loose causing the bad connection. If you suspect this I'd see if Moto will warranty the tray or if they are aware of any challenges on this device. Let us know what the outcome is.
Turn off phone, remove card. Turn phone on.
Reboot to safe mode - hold power button until power off shows up. Long tap on power off until safe mode prompt comes up. Acknowledge. In safe mode go to Settings>Storage>Internal Shared Storage. Tap on Cached Data. Tap OK to clear Cached Data.
Reinsert card. Wait to see if it is recognized. If it is, reboot your phone - hold down power button until screen goes black, then release. After phone is back on, wait to see if card is recognized. If it is, try to look at your goodies. If they are there, VIOLA!
If the card is not recognized or you still cannot look at your stuff, then something else is going on and you may, indeed, need a data recovery service.