So I took one of my external HDDs (total of 360G capacity with about 100G remaining) and issued the command to let it be used as a SWAP space.
The antecedent of "it" is unclear, and the answer to your question depends on that detail:
"It" = 100GiB Free Space
If "it" refers to the 100GiB of free space you mention, then the appropriate commands would have been:
parted, GParted, or some other tool to create a new partition in that unpartitioned space.
mkswap or GParted to prepare the new partition as swap space.
swapon to activate the swap space.
There are variants of this. For instance, you might have created a swap file rather than a swap partition. In any event, the key point here is that only part of the disk was used as swap space, leaving the used portions of the disk untouched by Linux's swap tools.
In this case, your original data should be accessible. If it's not, further diagnostics are required, as noted below....
"It" = Whole Disk
If you did not prepare a swap partition or swap file, and simply issued
mkswap on the whole-disk device (
/dev/sdb or whatever it is) or on the existing partition(s) on the disk (
/dev/sdb1, for example), then you've destroyed at least some of your existing data. You might be able to recover some file using a tool such as PhotoRec, but how many files you'll be able to recover depends on how much swap space your software consumed while you left it running. If little swap space was used, you might be able to get back most of your files; but if your software chewed up most of the available disk space, or if you were simply unlucky in what specific sectors it used, you could have already lost most or all of your files.
If the damaged disk used NTFS, note that there are Windows-specific programs similar to PhotoRec that do the same job, and may do it better. The times I've used it, PhotoRec has never recovered filenames for me; but some Windows-specific tools may do so. Thus, you may want to look into such tools.
In Either Case....
There are two commands that you may want to run if you're not sure what you've done:
sudo parted -l to learn how your disks are partitioned.
sudo blkid to learn how each partition is prepared (what filesystem it uses, or if it's swap space).
If you're not sure how to interpret the data, edit your question to add it or post a link to a pastebin site that holds the output.
These commands may turn up the cause of your problems if you did not wipe it all out as swap space. You might need to do something more in that case, though. For instance, if your external disk uses NTFS, you might need to run
CHKDSK on it from Windows. (There are no adequate NTFS-repair tools in Linux, so a system crash when NTFS is mounted requires repair in Windows.)