When you say you were 3.5 weeks pregnant do you mean you miscarried 3.5 weeks after your BFP?
It's my understanding, though I may be wrong is that a chemical miscarriage is when a woman's period arrives pretty much arrives on time and the only reason the woman knows she ever conceived was because she tested early.
If a loss occurs a week or so after a BFP then I would class that as an early miscarriage, not a chemical pregnancy.
I have only had one early loss where I was getting positive tests for 2 weeks after my initial BFP but then they started fading until eventually they were negative and I miscarried a few days later.
My cycle returned to normal straight away.
I have always tested early and I do see the benefit of it because even if it does end up as a chemical and the period arrives on time (ish) then at least the woman knows that she can conceive.
A woman who doesn't test early and so has her periods on time may wrongly think she hadn't conceived, or medically can't conceive, when in fact she can but the eggs just fail to implant correctly.
Inability to conceive at all and ability to conceive but eggs that not able to implant are two different problems and I think it's beneficial to know which (if any) you're dealing with.