Hi Lulie, welcome to the group. Really glad you reached out for support after what happened with your sister. The unpredictable outbursts and uncontrolled emotions coming from a pwBPD (person with BPD, or BPD type traits) are totally disorienting and devastating. I'm so sorry you went through that.
This is a group that "gets it". Nobody here is going to say "why weren't you nicer" or whatever. It's a whole different ball game with PDs, and approaches that "work" with "normal" people are often ineffective at best with PDs. The tool and skill set for responding to PD behavior is often unintuitive but over time can change the relationship to be "less worse". Fortunately you don't need agreement from the pwPD for you to work on things!
You mention wanting to find a professional in Texas; have you seen the Psychology Today "therapist finder" yet? You can specify what location you want, and then there is a drop-down menu on the left called "Issues" where you can specifically select Borderline Personality Disorder.
https://www.psychologytoday.com/us/therapists/texasHonestly I'd recommend you and your family getting support from the therapist, rather than trying to "convince" your sister to go. I'm sure you can imagine how that would play out

It doesn't mean "you're the problem" if you go. In fact, having a professional, neutral third party, with experience in PDs, can help you and your family walk through this while keeping YOUR health and YOUR sanity.
Let us know if that link works OK for you. And come back and post whenever works for you -- I know it's been tough finding open therapists/counselors these days, so we are here to talk through what's going on, whenever you want.
Keep us posted, and again, welcome;
kells76