Unless your girlfriend has
teeth "down there" or is wearing uncommonly sharp "body jewellery", I cannot see how you could make a distinction that the injury you suffered was a cut and not a tear.
I suspect you are trying to convince yourself that it will heal nicely and not cause a "scar" that is "weak" and "prone to tear again". Your reference to "frænulum breve" does tend to "give the game away" to me at least, and indicate that you have been reading around on the Internet, found some nasty sites and have managed to collect a number of unfortunate and really unhelpful concepts such as the "prone to tear again" notion.
I put it to you that you
tore your foreskin. This
would have happened because you were a bit too vigorous and your girlfriend, not having given birth to a baby yet is still rather pleasantly "tight"
and on these occasions was not as sexually excited as you might have expected, and so was lacking her natural lubrication. As Jim alludes, it tends to suggest you were not using a condom because the condom tends to mitigate the force applied to your frænulum and frankly it concerns us that you might not have been wearing a condom as doing so is on the one hand important in preventing the spread of sexually-transmitted diseases in other than lifetime-committed relationships
and on the other hand, an important "back-up" contraception where the young(?) lady is not using a guaranteed contraception such as the Implanon® device.
The GP has probably never
heard of "frænulum breve" because it is not part of a normal medical training. He
hasn't been trawling the 'net for fetish sites (or at least, not this sort

) and therefore hasn't come across it. Sure, he has perhaps come across one or two chaps who have torn their frænulum and might be considered on that account to have a somewhat
short frænulum, but quite appropriately said "OK, well you tore it, just let it heal" and thought that if it tore enough, it would end up a bit longer when it healed and would (eventually) not be as easily injured in future.
The term ("frænulum breve") is really more part of a rather off-stream or what I would tend to call "fetish" culture of people advocating circumcision on its purported "merits" and serves as a common "excuse" from such people for surgery. As such they dwell on how
bad this supposed medical condition is, how many problems it causes you, how it tends to get worse if not "treated" and how you almost always need to have surgery for it.
We on the other hand say - as Jim has - OK, let it heal for starters (but don't give it
too long - a week is plenty) and get going on the stretching exercise -
as you would have found advised over and again reading back through this discussion board. Indeed, what we advise in virtually every case applies - you probably need to do the "exercise" to stretch your foreskin a little so that it slides back comfortably
as well as the one for stretching your frænulum, and you
will need to do it - persistently - for a while!