Dont create your own graphics object, use the "e" argument that passed into the Paint event, it contains the graphics object:
Private Sub PictureBox1_Paint(ByVal sender As Object, ByVal e As System.Windows.Forms.PaintEventArgs) Handles PictureBox1.Paint
e.Graphics.DrawString("AntyText", New Font("Comic Sans MS", 20), New SolidBrush(Color.Black), 5, 5)
End Sub