Yes it is possible to perform the RCT through the existing bridge but sometimes we need to remove the bridge to gain access to the decayed part of the tooth.You need to go to an Endodontist.
Yes definitely if abutment tooth is infected it will require RCT if the prognosis of saving this tooth is good. Important thing to note is whether to retain present bridge or not. One of the common causes of a tooth acquiring infection is because of inappropriate crown and tooth margin. If a dentist assesses that the crown is good and do not require correction than RCT can be done through existing bridge or else it is advisable to get your bridge removed and get a new one after RCT is completed.
Go to an endodontist and get yourself examined clinically and radiographically.
Don't postpone seeking an expert advise or you risk losing your infected tooth and bridge work.