You can override SetBoundsCore and make it to use height of ComboBox as height of your control:
protected override void SetBoundsCore(int x, int y, int width, int height,
    BoundsSpecified specified)
{
    base.SetBoundsCore(x, y, width, comboBox1.Height, specified);
}
Note 1: If your UserControl contains just a ComboBox, it's better to derive from ComboBox rather than creating a user control containing a ComboBox
Note 2: You can make it obvious in the designer that control can just resized from left or right by creating a new ControlDesigner and overriding SelectionRules property. To do so, add a reference to System.Design assembly and then create a custom designer:
using System.Windows.Forms.Design;
public class MyControlDesigner : ControlDesigner
{
    public override SelectionRules SelectionRules
    {
        get
        {
            return SelectionRules.LeftSizeable |
                   SelectionRules.RightSizeable |
                   SelectionRules.Moveable;
        }
    }
}
Then it's enough to decorate your custom control with designer attribute this way:
[Designer(typeof(MyControlDesigner))]