You do not have to allow the label of your personality disorder to bring you down and prevent you from achieving beautiful things, happiness and success in your life! Do not listen to anyone who tells you otherwise. We can achieve anything we set our hearts and minds to, we are people, and loving and sensitive people at that - just because we have BPD doesn't mean we cannot help others. In fact, I think BPD patients are capable of being the most beautiful and loyal healers.
Do you want to know what I think?

I had the unfortunate experience of being hospitalized in some places, and the best nurses and staff that I came across, were not the text book types that had no clue what it was like, but those who had been through some hardships themselves and were more personal with me - there needs to be more individuals like yourself who are helping people.
Don't ever feel bad that you are using your gifts - though at times may seem like a curse - to help people, there is nothing two faced or double lifed about that, it's honourable and amazing.
Do not ever feel guilty or bad about what you have come through and what you've owned. Realize that your patients will respect you, open up to you, and trust you even more than your other co workers because you have been there.
I'm betting you too would feel more at home with someone who's experienced something similar, than with someone who hasn't. In a world where most of the mental health systems are corrupt, you can bring something beautiful to it - because you do know what it's like.
It sounds like you are self aware and honest with yourself, which is a plus!
When it comes to your own health, it's very crucial to take into consideration how you feel. I'd say list out the pros and cons. It sounds to me like it's a very big passion of yours to work there and help people. I'd say it sounds more like you are allowing other peoples fears bring you doubt.
I'm guessing SH = self harm? That worries me that you are currently indulging in this behaviour, and you would think it would not look so good being in your career if your employers or patients were to find out. That is not as professional, especially if you are working in a hospital setting. I think it is definitely something you need to work on, but in the meantime, don't beat yourself up about it. Everyone struggles with something - everyone.
I don't think it's exclusive to BPD, but it is something I used to struggle with a long time ago and I treated it similarly to an addiction and was able to recover from it.
I'm not sure if you are ready to hear this, but alternative recovery methods such as the 12 steps worked great for me.
I've been working as a paramedic in training. I have a pretty extensive background however, and it was my history of alcoholism that was my employers main concern and that I confessed to.
But what they do not know, was that along with my BPD I also suffer ASPD and something wrong with my DNA makeup LoL that made me quite murderous back in the day, among other disturbing things but seriously, people change.
Naturally you would think yikes, why would you have someone like that in the job of healing people and being around injuries?
But do you want to know how healing people helped me?
Because when I began to learn about anatomy of the human body, it made me appreciate the inner workings of the human body. I no longer viewed the body as just a meaningless blob of flesh (that was so easy to harm). I got to see and learn that the human body was so complex and beautiful, like this beautiful matrix of creation, and that in itself seemed so intricately designed that it only proved to me the existence of a soul, and to me that is more important than anything! And so beautiful!
I need to have faith as without it I am a basket case.
When I learned about first aid, my focus was no longer destructing myself or others, but was to help them. It's simple really - when my focus is to heal, I no longer have any room to focus on negativity.
Granted my recovery did not happen from taking a first aid course, nor did it happen overnight.
I think to work there you would need to set a good example and if you continue to work in that career you might learn to, and because of this, it might help you.
You started this question off about your career placement, but the real issue is what you are struggling with, granted if you found a way to cope with it properly, you wouldn't need to choose between your job and what you love to do.
You may be around people who harm themselves, but if you think about it, though it may trigger you, it should also make you feel responsible for proving to them that they can get through it. You would think that this in itself would make you feel stronger in yourself to overcome your problem.
But I guess if its making you feel weaker, then you might have to accept its not a good fit for you right now.
In all, it's up to you. I'm just throwing words around on a computer screen to help you brainstorm ideas, I hope you sort it all out!