You will need a glass jar that will hold one quart, must have a cover!
Bring the vinegar, water and sugar to a boil in a saucepan, stirring constantly until the sugar is dissolved. Take the saucepan off the heat and set the liquid aside to cool to room temperature.
Open the jars of herring and drain them in a strainer. Pick out the herring fillets, rinse them in cold water, and throw everything else away.
Cook the carrots according to the package instructions, but make sure they're still firm and not soft.
Peel the red onions and cut them into thin slices.
Arrange one-fourth of the onions in a thin layer in the bottom of the 1-quart glass jar. Top them with a third of the herring. Top the herring with a third of the carrots. Place 2 or 3 dill springs on the top and scatter on a third of the allspice and a third of the mustard seeds. Repeat the sequence until all the ingredients have been used, ending with a top layer of onions.
Pour the cooled pickling liquid into the jar. It should just cover the contents. If there's not enough pickling liquid, top off the jar with a little white vinegar right out of the bottle.
Place the cover on the jar.
Refrigerate the herring for 3 days before serving.