If she was previously worked for a salon, then suddenly having to go full time self employment, it would have been a big change to her. Likely, it has taken her awhile to get her act together.
Many people find getting to grips with the business side of things hard (I was in a similar place, myself, and felt really overwhelmed).
Ignore that told you, that she would call you, ‘when sorted’, she probably said that to lots of people(and indeed meant it!), but since the seven months or so, she’s lost the list of contact details. OR, I know in her position, I would think that people may have already sorted out their nail needs, and I would feel a bit like I was cold calling.
It’s also down to the customer, who knows when their nails need doing, so as soon as you see her business advertising, that’s the time to call.
Often when a new business starts, it’s common for there to be a a flurry of bookings at the beginning (eg everyone’s curious about new and shiny things😃). So, I doubt she is lying about September being her next free dates, especially as your nails sounds like they take awhile to do.
I would check price, and and then book a September date, asap, because who knows, if you leave much longer - Christmas will end up being the next she offers😝
If she cancels the September date, then, I think you’ll have the answer.