Are trailer hitches all a standard size and fit?

The reason I ask is because on my bike, due to a broken screw, the baggage carrier is attached to the screw holes behind the axle that would normally be for the rear mud guard instead of the screw holes above the axle. This means that I have very little clearance between the tip of the strut of the baggage carrier and the axle. Therefore I don't want to spend a hefty sum of money on a trailer until I have first bought a trailer hitch on its own and verified that it will fit in the narrow space available between the axle and the tip of the carrier strut, assuming that the trailer I end up buying will attach to that hitch.

I know that there are also trailers available that attach to the saddle post. The problem with those is that I have very limited storage space and I haven't come across one of those types of trailer that can be folded. So it looks like a trailer that attaches to the axle is my only option, if I can make the hitch fit.