First of all, I want to wish you & your baby all the best, you are so brave.
I had similar experinces as you, but not as scary.
I didn't know I was pregnant in the first ectopic pregnancy, I had light bleeding with dull pain for about a week ( I thought it was my M, but the bleeding or the pain didn't stop) I went to the hospital it was diagnosed ectopic, I didn't have the tube removed because the Dr said the tube hadn't burst & could heal. I regretted not having the tube removed because my 2nd ectopic was in the same tube. This time it was very painful, just like you, sweating, faint, weak and vomitting. The Dr found the tube had burst, and surgery was quicikly performed to remove the whole tube. It was a terrible experince, I cried so much.
Later I went for IVF, Dr said a scared tube would never heal completely, and it's best to remove it.
Dispite all the pain & sadeness, I now have two lovely kids, first one by IVF and 2nd one by natural cycle.