"In a low mood" is the correct grammar..although that is not a common expression..In a bad mood is much more common...Down in the dumps has been a common expression for many years which is equal to In a low mood..or I feel a little down today..."I'm having a rainy day" is common for some people..Clouds and rain and storms are often equated with "depression" or "sadness" I am glad to help..If you have further questions..just send them to me at [email protected] will be glad to help

Both acceptable. Wouldn't be too wrong without "a". I'm girl. I'm a girl. Sometimes you do that for some reason, some kind of emphasis. Just like "apple" doesn't have to always follow an "an".