I think you'll have to do some sleuthing. As in, ask a friend who you're pretty sure you sent an invite to - did you receive this? Don't be pushy; you're just asking for information (as you are here).
Next time - seriously - make a Facebook page for your art business. It won't be easy to convince everyone on your friend list to join it, but do it in small doses (as in, 20 - 50/day and no more). Start with the people who are your biggest fans and are most likely to spread your message/invitation to like the page. That's possibly your mom, but it's also your gossipy Aunt Margie who posts EVERYTHING on FB.
Once you've got a page (and when you get 30 people to like it, you can start getting metrics), you can add events easily and you won't have to send them to anyone.
Facebook is trying to do things with this restriction:
- It wants private individual accounts to remain for individuals and are not used for commercial purposes, as that prevents this precise situation, where you are stuck with manually inviting a ton of people and it's not targeted. It is in Facebook's - and yours, I might add - best interests for invitations like this to be targeted so that people don't feel like they're being spammed. And,
- Yes, Facebook would love to sell you advertising, in particular, ads which increase reach and engagement. But you won't need them, at least to start. Instead, pay attention to when your fans are online (another good reason to have a page and not use your private, personal account for such things) and target your messages to them and to the days and times they are on Facebook.