Just measuring the size of the bloom should eliminate all of the miniature rose possibilities, Zuzu, because miniature roses are classified by the size of the blooms.
For now, Divvy, take it slow and just work on getting your rose to come back. I'd like to suggest that you don't let the rose put energy into blooming, just new growth right now. By not allowing it to bloom, the plant will put it's energy into growing roots and foliage and becoming a stronger plant.
Looks like you have done a good work bringing it back. We will have plenty of time to help you find an identification when it stronger. Good work.
