Hello, T-Law, and welcome!
You've found a safe, supportive group here, with a lot of advice and tips to share.
You're not alone in not having an official diagnosis. My husband also has not been diagnosed. In fact, you'll see a lot of shorthands that look like this: uBPDw (undiagnosed BPD wife). Diagnosis of BPD can be quite tricky and many people here are not dealing with an official, diagnosed case. The good news is, though, that many of the tools and advice you'll find here can apply and help you, diagnosis or not.
As for getting her to recognize it, that's very tricky. The fact you were able to convince her to start seeing someone already puts you ahead of many here. Quite a few pwBPD are very reluctant to get help at all.
I would strongly recommend you not say anything to her about your suspicions. That rarely goes well. Better for it to come from a professional. Though, like I said, there are still things you can do to make your relationship and life better, even if there is no diagnosis.
Living with a person with BPD (or BPD symptoms) can be exhausting, I know. I've been there. Do you mind sharing a few more details? For instance, what are some specific behaviors that cause the most trouble in your relationship? If we know more we may be able to offer some more helpful advice.