As you are having bad obstetrical history with two previous abortion and one hydatidiform mole
, now your pregnancy is high risk pregnancy.
And in present pregnancy also you are having mild pain, which may turn into premature labor
That is why your doctor prescribed progesterone
Progesterone is essential to maintain pregnancy. These supplementary progesterones may increase the general pregnancy symptoms like vomitings, frequency of urination etc.
But no other serious side effects will not be there and baby will not get affected normally.
Take regular antenatal checkups and follow baby growth by ultrasonography