Extract time series from ImageCollection for multiple points - Google Earth Engine

I have the Sentinel 2 (COPERNICUS/S2) ImageCollection and a FeatureCollection of points. I want to extract a time series for each of the points from the band information in the ImageCollection.

So far I have the following code:

// Create a polygon to subset sentinel data 
var poly = ee.Geometry.Polygon(
        [[[13.932985323828689, -14.515258012418162],
          [13.932985323828689, -16.041324207881946],
          [15.690797823828689, -16.041324207881946],
          [15.690797823828689, -14.515258012418162]]], null, false);

// Import sentinel data
var sentinel2 = ee.ImageCollection("COPERNICUS/S2")
  .filterBounds(poly)  // TESTING - Filter by polygon
  .filterDate('2016-02-01', '2019-02-10');  // TESTING - Filter on date

// Create FeatureCollection of points
var features = [
  ee.Feature(ee.Geometry.Point(14.5, -15)),
  ee.Feature(ee.Geometry.Point(14.8, -15.1)),
  ee.Feature(ee.Geometry.Point(14.9, -15.2))
  ];

var points = ee.FeatureCollection(features);

// Define a function that works on a single point in the FeatureCollection
var pointExtract = function(feat) {

  // Get geometry of point
  var geom = feat.geometry();

  // Define a function that gets a point value for an image
  var pointGet = function(img, f) {
    // Duplicate feature
    var newf = ee.Feature(f);

    // Extract band value for pixel
    var value = img.reduceRegion(ee.Reducer.first(), geom, 30).get('B2');

    // Return as a string in the duplicated feature
    return ee.Feature(
      newf.set(ee.String(value)));
  };

  // Iterate over imageCollection to get time series
  var newfeat = ee.Feature(sentinel2.iterate(pointGet, feat));
  return newfeat;
};

// Iterate over points in FeatureCollection to extract time series
var output = points.map(pointExtract);

// Inspect output
print(output);

But I get the error:

FeatureCollection (Error)
Error in map(ID=2):
String: Parameter 'input' is required.

var site = ee.Geometry.Polygon(
    [[[13.932985323828689, -14.515258012418162],
      [13.932985323828689, -16.041324207881946],
      [15.690797823828689, -16.041324207881946],
      [15.690797823828689, -14.515258012418162]]], null, false);

var features = [
  ee.Feature(ee.Geometry.Point(14.5, -15)),
  ee.Feature(ee.Geometry.Point(14.8, -15.1)),
  ee.Feature(ee.Geometry.Point(14.9, -15.2))
  ];

var points = ee.FeatureCollection(features);
// Import sentinel data
var sentinel2 = ee.ImageCollection("COPERNICUS/S2")
  .filterBounds(site)  // TESTING - Filter by polygon
  .filterDate('2016-02-01', '2016-10-10');  // TESTING - Filter on date

// Set center Object
Map.centerObject(site);

// Time series at the identified points
var chart = ui.Chart.image.seriesByRegion(sentinel2.select('B2'), points, ee.Reducer.first());
print(chart, "Sentinel2TimeSeries");