I am 23 weeks and 4 days pregnant with a girl. My cervix is 2, 6 cm. Should I worry and start taking progesterone related drugs? If yes which one is best?

See your doctor . Unfortunately you cannot be helped online, you need to be seen, examined and assessed by your obstetrician, you can't just self treat, your doctor would decide which line of therapy that suit your case, good luck .
Cervical length. Cervical length is one metric than can be used to assess ones risk of preterm labor. The management depends on the patients past history. In someone with a history of preterm birth Progesterone injections are used. In someone without a history sometimes vaginal Progesterone is prescribed. Many doctors used a cutoff of < 2.5 cm. Discuss the options with your doctor.
Pregnant. What is your past history with pregnancies? Have you had any miscarriages? Consult with us to help you determine when to take progesterone if needed.