For what it’s worth… back before we were married, our diocese offered a class in the Billings method. Seemed pretty simple. We were also pretty “conservative” in how we applied it, gave an extra day or two of “cushion” on either side of the fertile period. However 3 of our 4 conceptions happened during months when the symptoms & charting said that conception was unlikely. Now I can’t call that a failure of the method; the kids are wonderful and a gift from God. However, if (as you describe) having another child could be very bad for your health & well being and for your family, I offer my experience as one of the 1% or 2% or 10-15% or whatever statistics you believe, where NFP would not be helpful in avoiding pregnancy.
And there are people out there who will say “you must not have done it the right way” or something like that, which is not so helpful - as I say, we were quite “religious” about how we did this. And others will say “instead of Billings use xyz or abcde method!” Which is fine and helpful advice, except it is retrospective in nature… you don’t know that a particular method didn’t prevent pregnancy, until after it happens.
A final point - when anyone gives you advice based on personal experience - as helpful and well-intended as it is, remember that it is anecdotal. That includes mine. Your results may be the same, or different.