Body needs some time to get use to the hormones from outside. Most common side effects from depo contraception are irregular vaginal bleeding. Some of your symptoms (extreme exhaustion, mood swings...) could be due to the hormonal contraception and other (flutters in stomach and a lot of gas) could be due to some digestive disorder. I don't believe that you are pregnant but you can do a pregnancy test for sure.
Effects of the depo contraception usually last 3 months. If you can't stand the side effects you may decide not to take another shot after 3 months.
Had you experienced digestive symptoms before received depo shot?