There are a few threads' worth of questions tangled together here, so let me try to untangle them, and please read all of this as general information rather than a plan for your own next cycle, which only your clinic can set.
The short answer: for most people there is no fixed number of months you are medically required to wait after a failed cycle, and the common idea that you must give your body three months to recover is not a rule so much as a rough comfort figure that has taken on a life of its own online. What there usually is, is a wait of at least one full menstrual bleed, and the reasons are specific rather than mysterious.
Beekeeperjo, on the drugs point: the medications used in a cycle, the stimulation injections, the trigger, the progesterone support, largely clear from your body within days to a couple of weeks, not months. So "waiting for the drugs to leave your system" is not really the thing holding you back, and it is one of the more persistent myths in this area. The wait is about two other things.
First, the lining. After a stimulated cycle and a transfer that did not work, your body needs to shed the built-up endometrium and reset, which is what that first bleed represents. Starting a fresh medicated cycle usually means beginning again from a known baseline, and most clinics time that to the start of a natural period, which is why "after a bleed or two" tends to land around four to six weeks in practice.
Second, and this is where it genuinely varies, the ovaries. If your cycle involved heavy stimulation, or if there was any concern about ovarian hyperstimulation syndrome, a clinic may want the ovaries fully quiet and any enlargement or fluid resolved before stimulating again, and that can push the gap to one to two months or occasionally longer. That is a real physical reason, not caution for its own sake, and it is one of the situations where the wait is not optional. It is worth knowing what OHSS actually is if that word came up for you at all.
A few things that surprise people. Back to back cycles are a real and reasonable option in some situations: a frozen embryo transfer asks far less of the body than a full stimulated cycle, as gemma_ttc found, and in certain cases clinics even stimulate twice in one cycle on purpose to bank more eggs, so "going straight back in" is not automatically reckless. Equally, a failed cycle is often the point at which a clinic wants to change something (the protocol, the medication doses, adding a test) rather than repeat the identical cycle a fortnight later, and that review is frequently the reason for the pause, not any harm in speed. The emotional side is a separate clock entirely and does not have to match the physical one in either direction: some people are steadier going quickly, some need a real break, and neither is the correct answer.
What none of us here can tell you is which of these applies to your two cycles specifically, or what 37 and a fresh negative mean for your particular next step, because that lives in your chart and not in this thread. Your follow-up consultation exists precisely to ask "why this wait, and could we go sooner", and it is a completely fair question to put to them directly. The site's guide to dealing with a failed IVF cycle covers the questions worth taking into that appointment, and if a frozen transfer ends up being part of the plan, how a frozen embryo transfer works explains why the timing there can be so much more flexible.
