There are a couple of possibilities. The cement that was used maybe causing the sensitivity, the nerve maybe inflammed from the preparation of the teeth, or the crowns do not fit. Root canal therapy is a viable treatment but I can not tell you if that is necessary or not. I think the amount of discomfort you are experiencing is a determing factor and whether or not you want to seek out another opinion which you certainly have the right to do.
how long ago did you get this done? I had a molor done about 2 months ago and at first it was sensitive(no root canal) but now it is fine.
you should ot need anything done to a crown so soon after it is cemented. I have no idea what a poecelain filling on or around a crown is, but i suspect what yu are saying is that the dentist placed some sort of "sealig" material around the edges of your crown. Again, if all is well and if all was done correctly with your crown, you should not need this. I also suspect that if you are having sensitivity it may be due to poor margins (the edges of the crown may not extend far enough and may not be well adapted to the tooth) At this point, I'd get another opinion about why you are having this problem, and about the quality/integrity of the work that was done.
See my comments in the thread on this forum about putting crowns on live teeth.