You can loop through points and try to find the one by searching x value. If the point is not found, calculate y value based on the next and the previous ones. The below algorithm should work fine for line series:

const x = 3;

const chart = Highcharts.chart('container', {...});

const points = chart.series[0].points;
let prevX, nextX;
let prevY, nextY;
let y;

points.forEach((point, index) => {
  if (point.x === x) {
    y = point.y;
  }

  if (point.x > x && !prevX) {
    nextX = point.x;
    prevX = points[index - 1].x;

    nextY = point.y;
    prevY = points[index - 1].y;
  }
});

if (!y) {
  const xDiff = nextX - prevX;
  const yDiff = nextY - prevY;

  const unit = yDiff / xDiff;

  y = (x - prevX) * unit + prevY;
}

console.log(y);

Live demo: http://jsfiddle.net/BlackLabel/uavrmLhk/