Quote " I'd like to somehow export just the edits I made to some photos into a new catalog I made containing the same photos. Is there a way to do this?"
Since you are a new user to Lightroom I would suggest you have a look at some of the video's that are available so you can become acquainted with how Lightroom operates. See below for some hints.
a. With respect to your specific question it is important to understand that Lightroom Catalogs do not "Contain any original photo files". The actual image files are located in folders on your computer HDD where they were when you "added" them to the Catalog or where you decided to "copy" them when they were imported into the catalog.
b. To wit the Catalog file only contains data about the location of the Image File and other work you have done with the file after import.
c. Lightroom is designed by default to work with a single Catalog and you can have your image files stored in folders on your internal HDD, External HDD or Network Drive.
d. Lightroom can only work with one Catalog at a time so working with multiple Catalogs only complicates the workflow.
Ok so that said to achieve what you require you can select the photos from one Catalog and do an "export as a catalog" then select/open the catalog you wish to include the selected files and do an " import from catalog (the catalog referred to above. This requires Lightroom to shut down and reboot.
The better option would be to have one Catalog and work with Collections, Smart Collections to segregate groups of photos. Collections and Smart Collections do not actually contain copies of the image files its just data in the Catalog file. This way you only have ONE master image file which can be connected to multiple collections.
Within the Catalog file you can also make "Virtual Copies" which reside alongside the original image file. Here again they are virtual i.e. data info in the Catalog file not an actual copy taking up additional space on the HDD.
Excellent answer, DdeGannes!
Matai, some photographers do require multiple catalogs for their work - however using one master catalog with collections and/or virtual copies makes much more sense when you are using the same original photos.
Be sure to back up your Master Catalog often and preferably to a different drive. That catalog has all your edits and variations on photos. You should also make a back up of your original photo files to a separate drive. That way, if your main drive were to have a problem, you always have a copy of both the Lightroom Master Catalog and your photo files.