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It may be a nitrogen/phosphorus imbalance in the soil. Too much nitrogen and too little phosphorus can result in little to no blooming, which means no fruit. This article should help: https://www.gardeningknowhow.com/edible/fruits/figs/fig-tree-is-producing-fruit.htm

Figs have a white sap and when it dries, there will be a slight indentation where the stem was cut.

Figs traditionally wait until the last minute to start filling out and ripen. In zone 6b, we are lucky when there is an early spring and late frost so there can be a decent fig harvest. Here is a link to a page of articles about figs: http://www.google.com/cse?cx=012078378210706707791%3Af1h5n_k1r5e&ie=UTF-8&q=figs&oq=&gs_l=#gsc.tab=0&gsc.q=figs&gsc.page=1

It sounds like you may have a wound canker at the base of the tree.  It is a common ailment for trees where weed wackers or lawn mowers have done some damage to the bark at the base of the tree.  The wounds allow fungus to get in.  Treat the area with fungicide and use a plastic collar around the base of the tree to protect it from further damage.

You do not need another fig in order for this tree to bear fruit. There are actually various reasons, as to why the tree may not be producing, and pinpointing the cause is the only way to fix the issue. This article should help you with that: https://www.gardeningknowhow.com/edible/fruits/figs/fig-tree-is-producing-fruit.htm

What likely happened, was due to the warm winter, the figs started forming too early. I would bet that you had warm weather alternating with a light frost. A light frost would not be enough to kill the leaves and the branches, but would harm the fruit. The fruit was killed by the frost. It is unavoidable and is a downside of a warm winter. The tree should try to develop a second crop shortly though, so you may still get a harvest this year, though it will likely be smaller than it has been in the past few years.