Binding issue in UserControl

I'm trying to achieve something that should be pretty simple but I'm stuck.

Here what I'm trying to do: a UserControl that is just a FontAwesome icon in front of a border.

Here the xaml of my UC

<UserControl
x:Class="Project.Views.UC.UC_CircledIcons"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
xmlns:local="using:Project.Views.UC"
xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
mc:Ignorable="d"
xmlns:fa="using:FontAwesome5.UWP"
DataContext="{Binding RelativeSource={RelativeSource Self}}"
d:DesignHeight="200"
d:DesignWidth="200">
<Border Style="{StaticResource BorderStyle1}"  Height="{Binding Height}" Width="{Binding Width}" BorderBrush="{Binding MyColor}" VerticalAlignment="Center" HorizontalAlignment="Center">
    <fa:FontAwesome Foreground="{Binding MyColor}" Icon="{Binding MyIcon}" Height="{Binding Height}" Width="{Binding Width}" FontSize="{Binding MyFontSize}" VerticalAlignment="Center" HorizontalAlignment="Center"></fa:FontAwesome>
</Border>

Here the cs code of my UC :

namespace Project.Views.UC
{
    public sealed partial class UC_CircledIcons : UserControl
    {
        public UC_CircledIcons()
        {
            this.InitializeComponent();
            this.Height = 200;
            this.Width = 200;
        }

        /// <summary>
        /// Le font size de l'icon est égal à 2.6 fois sa hauteur
        /// </summary>
        public double MyFontSize
        {
            get
            {
                return (double)GetValue(HeightProperty) / 2.6;
            }
        }

        /// <summary>
        /// Pour setter l'icone FontAwesome du composant via l'enum
        /// </summary>
        public static readonly DependencyProperty IconProperty = DependencyProperty.Register("MyIcon", typeof(EFontAwesomeIcon), typeof(UC_CircledIcons), new PropertyMetadata(default(EFontAwesomeIcon)));
        public EFontAwesomeIcon MyIcon
        {
            get
            {
                return (EFontAwesomeIcon)GetValue(IconProperty);
            }
            set
            {
                SetValue(IconProperty, value);
            }
        }

        /// <summary>
        /// Pour setter la color du border et de l'icone en même temps
        /// </summary>
        public static readonly DependencyProperty ColorProperty = DependencyProperty.Register("MyColor", typeof(string), typeof(UC_CircledIcons), new PropertyMetadata(default(string)));
        public string MyColor
        {
            get {
                return (string)GetValue(ColorProperty);
            }
            set {
                SetValue(ColorProperty, value);
            }
        }
    }
}

This is working fine if I use my UserControls statically in my xaml page like this:

<uc:UC_CircledIcons MyColor="#321654" MyIcon="Solid_Check"></uc:UC_CircledIcons>

But I'm trying to dynamically set the color and the icon of this UC. So I want to use binding to achieve this. Something like :

<uc:UC_CircledIcons MyColor="{Binding MainIconColor}" MyIcon="{Binding MainIcon}"></uc:UC_CircledIcons>

Like I'm doing with any Textblock content by binding to any property of my ViewModel. But with my UserControl this is not working. In the output windows i can see the binding error :

Error: BindingExpression path error: 'MainIcon' property not found on 'Project.Views.UC.UC_CircledIcons'. BindingExpression: Path='MainIcon' DataItem='Project.Views.UC.UC_CircledIcons'; target element is 'Project.Views.UC.UC_CircledIcons' (Name='null'); target property is 'MyIcon' (type 'EFontAwesomeIcon')

And I believe this is caused by the line :

DataContext="{Binding RelativeSource={RelativeSource Self}}"

In my UserControl's code. It seems like xaml is looking for a property named MainIcon in my USerControl's definition or this property is part of my ViewModel.

Where am I missing something ? Is there any way to achieve what I'm trying to do ? Thanks a lot for help.