Can a chipped molar be restored with resin?

Bonding can be used to repair a chipped molar. However, it may not last. A chipped molar is better repaired by porcelain in the form of porcelain onlay or a crown. 

Probably! But how long will the "filled" molar last? The real question is what are you thinking? Draining fistulas mean infection. The bacteria causing the infection can spread thru your bloodstream to other organs in your body. You are risking heart problems and stroke, amongst other things. Take this situation seriously and have the decay removed and a root canal and crown done, or have the tooth removed and deal with replacing it. What on earth are you thinking???

You've described a tooth that either needs to be taken out, or if there's enough tooth structure left you can save it with a root canal build up and crown.I would recommend getting this taken care of as soon as possible, since you've indicated a chronic infection.Your mouth is connected to your body, so the infection can spread.Sincerely,Dr. Reiser

If the tooth died and you never had a root canal then it's going to have to have a root canal or be extracted. You cannot leave a tooth in that condition untreated, or you risk a severe infection that could become life-threatening. Once the tooth has had  root canal therapy it would have to have a build up restoration and a crown. If it's extracted then your options would be an implant with a crown or a bridge or a removable partial denture. You've been very lucky that the infection has not yet progressed to the point that it could very easily get to. Please call the dentist immediately and schedule an appointment for evaluation and treatment.