"I'm wondering if any models or data provide predictions for the more immediate future, say 10 - 20 years from today."
"Specifically, I'd like to hear about predictions that directly influence humans, such as weather, flooding, disease, etc."
Basically, I take your question to be: "How are people affected by climate change today?" The expectation being that if present trends continue, the effects may intensify in the near-future (10-20 years.)
I suggest you consider how people today are affected by extreme weather, because climate change may manifest today primarily by leading to more intense and frequent extreme weather events.
This recent paper in Nature Climate Change, Attribution of climate extreme events (2015) proposes that 'snowmaggedon' in February 2010, superstorm Sandy in October 2012 and supertyphoon Haiyan in November 2013, and, in more detail, the Boulder floods of September 2013, may have been influenced by high sea surface temperatures that had a discernible human component.
In the popular article "Study sees a ‘new normal’ for how climate change is affecting weather extremes", an author summarizes some of the major conclusion of that paper.
For example, although a moderate storm "Sandy" may have occurred regardless of the effects of global warming, computer modeling suggests it is likely that global warming augmented this storm up to a level great enough to flood the New York subway.