Continue your regular allergy shots. If you take regular allergy shots and have no reaction to them, you'll need to continue them during your pregnancy. As always, your allergist will monitor your dose. Don't start allergy shots for the first time after you become pregnant. The dose should not be increased during pregnancy, but maintenance immunotherapy is safe and may allow you to require less oral medications.
Flu shots are a good idea for anyone who has asthma, and pregnant women are no exception.
In fact, if viral infections trigger asthma for you, then avoiding the flu is especially important. Some research has indicated that the flu might be particularly severe during pregnancy. The only pregnant women who should not have a flu shot are those who are allergic to eggs. Your doctor will probably want to wait until after the third month of your pregnancy to give you a flu shot. Although the flu shot will give you good protection from several strains of influenza, it can't protect you from all viral infections.