Hi,
The first thing I recommend looking at is your geoprocessing model - if you're able to share that here then we may be able to spot if there are any issues in the way it's setup.
Models are fine, but typically as your usage gets more advanced, you'll want to switch to Python scripts. I've shared an old example below. This uses a Linear Referencing tool as well, to add the distance along the line for each point (which I displayed in a client-side chart when you hover the mouse over). I would then add this Python script to a Toolbox and setup the input/output parameters (see image further below).
e.g.
import arcpy, math
inputLine = arcpy.GetParameterAsText(0)
inputRaster = arcpy.GetParameterAsText(1)
outputShapeZ = "in_memory\\outShapeZ"
outputShapeM = "in_memory\\outShapeM"
arcpy.ddd.InterpolateShape(inputRaster, inputLine, outputShapeZ)
arcpy.CreateRoutes_lr(outputShapeZ, "ident", outputShapeM, "LENGTH")
arcpy.SetParameterAsText(2, outputShapeM)
Thanks