Is this Time Salvager (2015) by Wesley Chu? It's the first book of a series by the same name.
Quoting the blurb from Google books:
In a future when Earth is a toxic, abandoned world and humanity has spread into the outer solar system to survive, the tightly controlled use of time travel holds the key to maintaining a fragile existence among the other planets and their moons. James Griffin-Mars is a chronman–a convicted criminal recruited for his unique psychological makeup to undertake the most dangerous job there is: missions into Earth’s past to recover resources and treasure without altering the timeline. Most chronmen never reach old age, and James is reaching his breaking point. On his final mission, James meets scientist Elise Kim, who is fated to die during the destruction of an oceanic rig. Against his training and common sense, James brings her back to the future with him, saving her life, but turning them both into fugitives. Remaining free means losing themselves in the wild and poisonous wastes of Earth, and discovering what hope may yet remain for humanity’s home world.
Google books has the first few chapters available to preview; James Griffin-Mars, the protagonist wears the near-invisible force-field suit ("exo band" for fighting, as opposed to "atmos band" for environment) in combat in the first chapter, and in the second he almost throws up because of "lag sickness."
In the third chapter Griffin-Mars reflexively activates his attack functions when he's disturbed by a maintenance worker, and hits him with a "kinetic coil":
Just as James was drifting off, someone shook him awake. On reflex, he powered on his exo band, expanded his field, and lashed out. The powerful exo-kinetic system-the military-industrial complex being on of the few industries still innovating-practically made him a god whenever he ventured back in time. The yellow glow of the exo sparked to life, expanding outward and slamming the intruder into the interior wall of the collie. A kinetic coil sprouted from it and wrapped around the man's waist. It squeezed.
There is a second book in the series, Time Siege, but it doesn't appear that there is a third book yet.