Travel to Indonesia is safe alone, even for a pretty young lady - That isn't your worry.
Staying in Jakarta is also safe, as long as you stay in good hotels, not cheap and nasty backpacker places.
If you arrive in Jakarta airport, use the taxi booking service as you leave the airport (Blue bird is best as they check their drivers' criminal records).
Syamsudin Noor Airport serves Banjarmasin, and is less that 20KM from the town.
I've never been to that town, but I understand there are several good hotels in that area.
There are Blue bird taxis in that town, you you should be fine.
http://www.bluebirdgroup.com/news-updat … -indonesia
If I can be of any help, I can try, but can't promise much as I'm really busy.
As for the boyfriend, this will sound harsh and horrible, but be careful he isn't scamming you - it would hardly be a fresh trick.
Look up the hospital on the internet, and call them before you do anything else.
Yes, I know I may be being a cad, but I have to suggest it, just in case.