从数据库中提取选项的变量选择元素

Been kinda stuck with this one for awhile.

I need my code to create 2 elements on a click of a button (Text input and Select). The Select element needs to be populated with values from a database. So far I've got this:

    <!DOCTYPE html>
<html>
<head>
        var counter = 1;
        var dynamicInput=[];

        function removeInput(){
            var elem = document.getElementById('ingredients');
            elem.removeChild(elem.lastChild);
            /*return elem.parentNode.removeChild(elem);*/
            counter--;
        }

        function addInput(){
            var newdiv = document.createElement('div');
            newdiv.id = dynamicInput[counter];
            newdiv.innerHTML = "Entry " + (counter) + " <br><input type='text' name='quantities[]'><select name='products[]'></select>";
            counter++;
            document.getElementById('ingredients').appendChild(newdiv);
        }
    </script>
    <?php 
        $link = mysqli_connect("localhost", "root", "", "cocktails");
        // Check connection
        if($link === false){
            die("ERROR: Could not connect. " . mysqli_connect_error());
        }
    ?>
</head>
<body>
<form method="POST">
    Ingredients:<br>
    <div id="ingredients">
        <div id="dynamicInput[0]">
            <input type="text" name="quantities[]"> 
            <select name="products[]">
                <?php
                    $sql = mysqli_query($link, "SELECT name FROM inventory");
                    while ($row = $sql->fetch_assoc()){
                        echo "<option value=\"".$row['name']."\">" . $row['name'] . "</option>";
                    }
                ?>
            </select>                   
            <button type="button" onClick="addInput();">+</button>
            <button type="button" onClick="removeInput();">-</button>
        </div>
    </div>
</form>
</body>
</html>

How can I populate the select that's created on a click of the button?

Of course whatever the user selects I will need to work with. How can I work with those values after?

Any pointers in the right direction will be greatly appreciated.