No, it isn't an std. It's an infection very much like thrush which can occur. It's an overgrowth of naturally occuring bacteria, although it's more common in sexually active women. I had this after I had my ius fitted.
I understand that some sources refer to it as an std but it isn't - if it were then both partners would need to be treated for the condition and, as you've said, it would be passed through sexual contact - that's untrue. I spoke alot to my doctor and the practice nurse about this as I was worried (having never even had thrush before) but it was impossible for me to have an std (checked before the insertion of my ius and also in a monogamous relationship who i've had checked lol).
In the most literal sense a sexually
transmitted disease is precicely that - passed on through sexual contact and bv isn't.
Hope this helps (and hope the anibiotics aren't to bad)