When you draw a shape it remains selected. It could be that the Bounding Box is getting in your way. The Bounding Box allows you to resize, stretch, or rotate selected objects.
Try going to View> Hide Bounding Box.
If you really want to keep the Bounding Box active on your shapes then deselecting your shape before you try making another shape will help. The previous answer gives a way to deselect. I find the fastest way is to hold the command/ctrl key down- this temporarily changes the tool you are using to your last used selection tool (white arrow or black arrow). Then just click on an empty section of your artboard (or even off the artboard) to deselect your shape, release the command/ ctrl key, and carry on drawing your shapes.