If the external hard drive worked fine on your Mac before, and after you dropped it, the drive turns out to be unrecognizable on your Mac, it is highly likely that the drive is physically damaged. What you should do is recover data from the drive with data recovery software or a local repair.
When Mac can't recognize the external hard drive, the drive may be greyed-out or unmountable in Disk Utility, and won't show up in Finder and Desktop, let alone access the data you stored in the drive, all the contents are at risk. The reasons behind an unrecognizable drive are various, but the one for your case should be physical damage.
After you dropped the drive, perhaps the sectors where the partition table, file system info, etc., stores may get corrupted so that Mac can't recognize the drive with such info. Disk Utility's First Aid can check logical and physical errors on the drive but can only fix some logical errors, it can do nothing with physical damage on the external hard drive.
However, as the drive still shows up in Disk Utility, it indicates Mac can detect it. Then you can try to recover data from the unrecognizable drive with data recovery software such as iBoysoft Data Recovery for Mac. Simply scanning lost/deleted files from the drive, previewing the results, and saving the wanted files to a different location can recover files from the not recognizing drive on Mac.
After recovering the data, you can try to format the external hard drive on Mac without data loss. Just give it a shot. If reformatting doesn't work, you can take it to a local repair for further help if you want to fix it, and the cost could be expensive.