My obgyn doctor suggest me getting progesterone shots once a week my first baby i had i delivered at 34 weeks should i get this shot? pros/ cons pleas

Yes: Your physician is correct. The american college of obgyn does recommend weekly Progesterone injections for those with a history of preterm birth. It is not associated with any fetal defects and does reduce your risk of preterm birth. In short, yes- it is recommended.

Get the shots!: 17-alpha-hydroxyprogesterone caproate weekly intramuscular injections between 16-37 weeks have been proven to prevent recurrent preterm birth by as much as 34-42%. They have only topical minor side effects from irritation, minimal cost (do not accept makena, ask for the compounded formulation) and are cost-effective for indicated use. Please heed your doctor's advice!