My new molar crown, infected, root canalled by hole, temporary filling fall out, so went different dr, is filling method same, if root canalled or not?

Is this the problem? 1) you had a new crown placed on one of your molars (was this a replacement for a previous crown that failed?) 2) infection then occurred, they did a root canal treatment& placed a temp filling which fell out 3) you went to new dentist, this treatment is possible: remove current crown, build up tooth & place new crown. Or if the crown is intact with just a small hole, fill hole up with composite.
Next? I am not sure of your question. It is common and usually not problematic to perform a rct through a crown. There may be some pain or discomfort for awhile but it should subside within a few days or week at most. Wether or not there is a temporary filling will not cause pain. The hole should be filled with a permanent filling as long as there is enough sound tooth structure present.