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[Reboh79]

redacted

[Zelot]

Just make a borderless textbox with a picture box beside it. If you highlight https:// you'll notice that your cursor stops just after the image and I assume that the image is not inside the textbox

[boops boops]

Dock a small PictureBox and your TextBox side by side in a Panel and make both child controls BorderStyle=None. BB

[bensonsearch]

just place a picturebox "inside" the textbox with transparent background and borders

[Joacim Andersson]

You can change the left margin of the text box with this code:

  Private Declare Function SendMessage Lib "User32.dll" Alias "SendMessageW" ( _
   hwnd As IntPtr, _
   wMsg As Integer, _
   wParam As Integer, _
   lParam As Integer) As Integer

  Private Sub SetTextBoxLeftMargin(textBox As TextBox, margin As Integer)
    Const EM_SETMARGINS As Integer = &HD3
    Const EC_LEFTMARGIN As Integer = &H1
    SendMessage(textBox.Handle, EM_SETMARGINS, EC_LEFTMARGIN, margin)
  End Sub

  Private Sub Form1_Load(sender As Object, e As EventArgs) Handles MyBase.Load
    SetTextBoxLeftMargin(TextBox1, 18)
  End Sub

Above I changed the left margin to be 18 pixels which gives me enough room to place a small picturebox inside the textbox.