Are you sure you actually managed to pick up the item? You should have seen a message saying "You have successfully taken a ___ from the Trash Isthmus."
Unfortunately there was an unusual glitch at reset which meant that the daily activities had to be reset manually. If you had already taken an item from the trash yesterday you may have been unable to take another today. I'm not sure whether or not the trash has been reset yet but if it has you should now be able to pick up an item with no problem.
However if you did manage to pick up the item, it is probably wearable so should have appeared in your Closet and most likely under the Head section of your wardrobe.
As for the pendant, what pendant is it? If it's a gender pendant then it should let you use it as long as you have a pet selected.
Hopefully this helped and sorry for any inconvenience caused with the glitch. ;w;