Do you consider a live birth after having a chemical pregnancy as a rainbow baby?

I haven’t gone to a doctor so never got hcg levels formally checked, last month I had a few faint positives and then wound up getting negatives and started my period late a few days after. I also threw up one day but it was unlike any stomach bug I’d ever had. But I’ve concluded that it’s very possible that I had a chemical pregnancy.

I’m wondering the views on rainbow babies if they’re only considered that after a miscarriage that occurred later on or not... i don’t want to seem dramatic or make a bigger deal of things than they are, but after ttc for 15 months for my first, i feel like I need to acknowledge that something possibly finally worked even if it didn’t last. I switch between being devastated to being unsure of how I feel because it was so very early. I’m clinging to the hope that studies show increased fertility in the months following a chemical.