Is it common to develop asthma during pregnancy?

No. Asthma may get worse, better, or remain the same in pregnancy but is not caused by pregnancy. Labetalol may or may not worsen asthma but does not cause asthma.
Asthma. Yes, it is common for patients to develop asthma in pregnancy. You are also taking a beta blocker for BP you may want your doctor to change it to another type of medication as non selective beta blockers can worsen asthma.