Haha, I felt silly because I had to download my own game to help troubleshoot. (I haven't actually touched it in years)
So, a couple questions, to clarify...
1. You're able to open the menu with "X" or "Escape" or by right-clicking, correct? If so, can you get to the "Equip" option without problems?
2. Do you have one of the following items: Fedora, Black Coat, or Flower Dress? Just checking as those are the only equippable items. If so, you should be able to equip via the Equip menu by selecting what body part to equip to, and then selecting what you'd like to equip.
I hope this helps, I'm not entirely sure what the specific issue is, so not sure what directly to recommend. Let me know if you still need help!