Ugh, that sounds like an awful experience! I'm glad you don't remember much of it.
What it sounds like is that you might have Endometriosis/scar tissue from your surgery. Your tubes might be fused to your uterus, which can prevent proper ovulation - but not always. You can still ovulate, but the tube needs to be able to move freely and receive blood flow to nourish the egg.
They might be able to see something with your HSG, but a Lap would be more thorough. My HSG didn't find my adhesions. I'm so glad I got the Lap. It's still good to run the dye through the tubes with the HSG though.
I can't say from personal knowledge specifically about Appendicitis, but I know from other ladies who had surgeries that ended up with scar tissue/Endo. It's weird, I never had surgery or an infection but I have adhesions and scar tissue all over.
I hope they get to the bottom of it and take care of it for you
It sounds like a promising reason as to why you haven't conceived yet...and it's fixable so that's awesome! I bet you'll be pregnant in no time! Still hoping for this cycle for you though. FX