I head breast MRI yesterday did the first part and then when dye was to injected the vein burst, with much pain, bleeding and swelling, we had to stop. Now they want me to com back after arm heals. I?

Ok. Sounds like you had a very unusual experience that is unlikely to reoccur. If the MRI is important for diagnosis probably should do.
Breast MRI. Unfortunately that occasionally happens with IV injections, it is very uncomfortable. However, the IV contrast is a critical component of a breast MRI for cancer detection. Without it, cancers may be missed, and other findings mischaracterized. A noncontrast scan is not sufficient. If you need to have the scan, you need to have it done properly. Please heed your doctpr's advice.