Options[extraAxisPlot] = {"AxisType" -> "xAxis",
      "AxisOptions" -> {}, "ExtraEpilog" -> {}};
extraAxisPlot[plot_, {axisStart_, axisFinish_}, {xpos_, ypos_},
    OptionsPattern[]] := Module[
    {printerPointsPlotRange, realImageDimensions, realPlotRange,
      plotRangeRatio,
      axisplotrange, axisxrange, axisaxes, insetpos, axis},
    printerPointsPlotRange = (#[[2]] - #[[1]] &)@(Rasterize[
                Show[#, Epilog -> {Annotation[
                        Rectangle[Scaled[{0, 0}], Scaled[{1, 1}]],
            "Two",
                        "Region"]}], "Regions"][[-1, 2]]) &;
    realImageDimensions = (#[[2]] - #[[1]] &)@(Rasterize[
                Show[#, Epilog -> {Annotation[

            Rectangle[ImageScaled[{0, 0}], ImageScaled[{1, 1}]],
                        "Two", "Region"]}], "Regions"][[-1, 2]]) &;
    realPlotRange =
      Module[{padding =

       Total /@ (Options[#, PlotRangePadding][[-1, 2]] /.
          None -> 0),
            baserange = (#[[2]] - #[[1]] &) /@ PlotRange[#], range},

     range = (baserange + padding) /. {a_ Scaled[b_] -> Scaled[a b],
                  Scaled[a_] + Scaled[b_] -> Scaled[a + b]} /. {a_ +
                    Scaled[b_] -> a/(1 - b)};
          range] &;
    plotRangeRatio = realPlotRange[#1]/realPlotRange[#2] &;
    {axisplotrange, axisxrange, axisaxes, insetpos} =
      Which[OptionValue["AxisType"] == "xAxis",
        {{{axisStart, axisFinish}, Automatic}, {axisStart,
            axisFinish}, {True, False}, {axisStart, 0}},
        OptionValue["AxisType"] == "yAxis",
        {{Automatic, {axisStart, axisFinish}}, {0, 1}, {False,
      True}, {0,
            axisStart}},
        OptionValue["AxisType"] == "Both",
        {Transpose@{axisStart, axisFinish}, {axisStart[[1]],
            axisFinish[[1]]}, {True, True}, axisStart},
        True,
        Print["Invalid axis type"];
        Abort[] (*If the option isn't one of the three axis types,
        then quit the code*)];

    axis = Plot[Null, {x, axisxrange[[1]], axisxrange[[2]]},
        PlotRange -> axisplotrange, Axes -> axisaxes,
        Evaluate@OptionValue["AxisOptions"]];

    Show[plot,
      Epilog -> { Evaluate@OptionValue["ExtraEpilog"],
         Inset[Show[axis,
             ImageSize ->
               plotRangeRatio[axis, plot] printerPointsPlotRange[
                     plot] + (realImageDimensions[axis] -
                     printerPointsPlotRange[axis]),
             AspectRatio -> (Last[#]/First[#] &)@(plotRangeRatio[axis,
                       plot] printerPointsPlotRange[plot])], {xpos, ypos},
           insetpos, Automatic]}]
    ];

test={{0.875,0.000361069,-0.137},{0.9,-0.000429778,-0.1096},{0.925,-0.000102596,-0.0822},{0.95,-0.000234415,-0.0548},{0.975,-0.00066855,-0.0274},{1.,-0.00114038,0},{1.025,0.00278551,0.0274},{1.05,-0.00148313,0.0548},{1.075,0.00132836,0.0822},{1.1,-0.000164138,0.1096},{1.125,-0.00036032,0.137}};

plot = ListLinePlot[test[[All,;;2]],Frame->True,FrameTicks->{{Automatic,Automatic},{Automatic,None}}];
extraAxisPlot[plot,{-.13,.13},{.875,.0031}]