Can my allergies & asthma go away after I am pregnant?

Yes. Allergic sensitivities often change in association with changes in hormones. The most common is during adolescence, but also after a pregnancy, and sometimes after menopause. Unfortunately, they can go either way - they may get better or may get worse - and there's no way to tell which way it'll go with any given individual.
30% chance. During pregnancy 1/3 get better with their asthma, 1/3 stay the same and another 1/3 get worse.