Your action will come before the foe's action next round.
It's a little unclear how that actually works with regard to everyone else involved in the combat. Since it says "you" it's implied that your initiative should be moved up to just before the foe, but it might be more sensible to move your foe's initiative down to just after yours.
It's a bit of a mystery, honestly.
I think your interpretation is more sensible. However, it does not say anything about the relative initiatives beyond yours and your opponent's. Say you're A, you have a friend B and your opponent is C. The result of the crit is that you (A) have initiative over C. It says nothing of your relative initiative vs B, nor of the relative initiative of B vs C. Presumably, those are unchanged.
If, in the next initiative roll, A rolls lower than both B and C, and C rolls higher than B, then you have a problem : according to the crit, A should go before C. According to the rolls, A should go after B. According to the rolls, B should go after C. This is not possible.
The way the crit result is stated implies that this is a duel (the PC and their opponent). It breaks down when there are more than two fighters because the crit results is expressed in relative terms.
Either the idea is that A feels inspired and "has the initiative" (over everyone else) and it should be stated explicitly.
Or the idea is that C has been shaken by the crit and has "lost the initiative" (vs everyone else) and it should also be stated explicitly.
The closest to your interpretation is the second expression (C's next initiative is lowered to the bottom of the initiative list). However, the wording seems to imply that the first interpretation is the correct one.
I would still lower C's init to the bottom of the list, though