@cue, I haven't heard of anyone fainting after taking Forteo. It does dilate your blood vessels, drop your blood pressure and increase your heart rate immediately after the injection. These effects can lead to imbalance. Usually you are back close to normal after 4 hours.
Pretty amazing that you ruptured your spleen by falling. It sounds awfully painful.
If you take the injection after a hydrating glass of water and a little salt, maybe an olive, you can mitigate the blood pressure drop. I'd go from 100/60 to 80/40 or 50, but I never felt it anything.
I'd say take the injection sitting down and then just be careful for a few hours. Don't move about too fast, plan one of your easy activities until you understand if and how if will affect your balance.
I hope this medication is as kind to you as it is to me. It's my favorite of all the medications because of the mechanism of action that builds strong integrated bones.