You are right in thinking that all will be well. This situation does resolve in time, and you now have the satisfaction of being assured that things are OK from a medical perspective. You have taken care of the necessary diagnostic work. Now the key will be to consult with the pediatrician and see if he/she wants to start your daughter on a regimen to promote regular bowel movements, in spite of your daughter's reticence. When children avoid bowel movements they are, of course, prone to constipation and impacted bowels. When they become constipated, bowel movements are uncomfortable, and this exacerbates the problem - they tend to want to persist in avoiding the bathroom. The importance of a regimen, undr medical supervision, of laxative and stool softeners is to avert constipation and impacted bowels and to promote bowel movements in the face of the child's reluctance. Be sure to schedule times to have your daughter sit on the toilet, and don't leave this to her discretion. Be patient and supportive and understanding, but do not cooperate with her avoiding the bathroom. With her pediatrician's help and your thoughtful approach, this will turn out OK.
Kudos and respect to you for not seeing this as an end-all-be-all problem! And for not seeing it as your problem, but as something she will eventually work through!! My oldest was on mineral oil from 9 months old to 6 years old. She is still prone to constipation, but knows how to handle it via diet now. (13 years old now)