Is a chemical pregnancy a miscarriage?

After nearly a year of trying, only 2 positive ovulation tests, and cycles over 6 weeks, we got our bfp about a week and a half ago. We were so excited but the lines kept getting more faint over the next 5 days, followed by cramps and bleeding 4-5 times more intense than periods. The doctor confirmed that it was likely a chemical pregnancy. Now I am left with all these emotions. I feel like we were robbed of that 1st exciting feeling to be pregnant. Why did this happen to us? Do I have a right to be sad? And is it fair to even call it a miscarriage and grieve since it was so early on? I’m worried if I tell people we had a miscarriage at 5-6 weeks that they’ll just say “oh that’s not a miscarriage or at least you weren’t that far along.” Looking for others that are feeling the same way I am or have been in this situation. Thanks <3