As far as I know, BIDMC doesn't have a dedicated Pediatric Pain service. Their Pain fellowship does offer exposure to the Pediatric Pain service at Children's Hospital, which is just down the street. This is limited to one month unless you use your elective to do Children's or you do the Longwood track. The best exposure you'd get in terms of Boston fellowships would be do to the Pediatric Pain fellowship at Children's Hospital.
As far as I know, the Children's program has only taken PM&R and Anesthesia residents. They offer one spot per year.
In general, I would say that the Pediatric Pain fellowships are not as competitive as the adult Pain fellowships programs. The fellows at BWH, MGH, and SRH have to spend a month and it's not a rotation most look forward to. I believe there are at least a few other Pediatric Pain fellowships out there. If you are interested in this field, I think the Longwood or Children's program would be ideal since you would get training in both Adult and Pediatric Pain.