Hi phonghue,
On button click you are redirecting before assigning session.
You have to first assign session and then redirect to page.
I have created a sample. Now take its reference and correct your code.
HTML
Page1
<table>
    <tr>
        <td><p class="padding2"><asp:LinkButton ID="lnkIndexAdminComp" runat="server" OnClick="OnIndexAdmin">* Administrative/Computer</asp:LinkButton></p></td>
        <td><asp:Label ID="lblAdmin" runat="server" Text="1" Font-Size="28px" Font-Names="Arial" Visible="false"></asp:Label></td>
    </tr>
    <tr>
        <td><p class="padding2"><asp:LinkButton ID="lnkIndexChildYouth" runat="server" OnClick="OnIndexChild">* Child/Youth</asp:LinkButton></p></td>
        <td><asp:Label ID="lblChild" runat="server" Text="2" Font-Size="28px" Font-Names="Arial" Visible="false"></asp:Label></td>
    </tr>
</table>
Page2
Message : <asp:Label ID="lblMessage" Text="" runat="server" />
Code
C#
Page1
protected void OnIndexAdmin(object sender, EventArgs e)
{
    Session["message"] = lblAdmin.Text;
    Response.Redirect("~/GlobalAgencyTemplate.aspx");
}
protected void OnIndexChild(object sender, EventArgs e)
{
    Session["message"] = lblChild.Text;
    Response.Redirect("~/GlobalAgencyTemplate.aspx");
}
Page2
if (Session["message"] != null)
{
    if (Session["message"].ToString() == "1")
    {
        lblMessage.Text = "Adminstrative/Computer";
    }
    else if (Session["message"].ToString() == "2")
    {
        lblMessage.Text = "CHILD/YOUTH";
    }
}
else
{
    lblMessage.Text = "";
}
VB.Net
Page1
Protected Sub OnIndexAdmin(ByVal sender As Object, ByVal e As EventArgs) Handles lnkIndexAdminComp.Click
    Session("message") = lblAdmin.Text
    Response.Redirect("GlobalAgencyTemplate.aspx")
End Sub
Protected Sub OnIndexChild(ByVal sender As Object, ByVal e As EventArgs) Handles lnkIndexChildYouth.Click
    Session("message") = lblChild.Text
    Response.Redirect("GlobalAgencyTemplate.aspx")
End Sub
Page2
Protected Sub Page_Load(ByVal sender As Object, ByVal e As EventArgs) Handles Me.Load
    If Session("message") IsNot Nothing Then
        If Session("message") = "One" Then
            lblMessage.Text = "Adminstrative/Computer"
        ElseIf Session("message") = "Two" Then
            lblMessage.Text = "CHILD/YOUTH"
        End If
    Else
        lblMessage.Text = ""
    End If
End Sub
Screenshot
