Yes, I think that's the problem. when I try to search for interstage shell parts nothing appears, only the fairings parts appear.
What i'm trying to do is something like this, but the top of the fairing stays attached to the upper stage of the rocket and won't let the stages separate. The only way I have found is to increase the width of the fairing, but it is unsightly.
https://imgur.com/a/DWZRbJM