Yes it is possible for you to get influenza A twice in a year.
You can have the flu virus more than once in a year because there are multiple strains of the flu virus that goes around.
I've gotten Influenza A twice myself and it was not good.
I've also gotten the flu 6 times in a single year which was even worse.
I came out of it okay afterwards though but I never thought I could get the flu virus more than once in a year and even more so never thought I would get the flu 6 times in a single year but it's possible.
It takes between 1 week to 2 weeks to get over influenza type A.
Getting over influenza type A takes the same amount of time to get over as it does to get over any other type of flu virus.
When you have the flu including influenza type A you're usually contagious with the influenza type A the day before you show symptoms of the influenza type A flu virus.
That means you could infect someone else around you without even knowing about it.
Most people when they do have influenza type A get feeling better within 1 week to 2 weeks after they get it.
If not you need to see a doctor about it.
However a doctor cannot do much for the common flu and usually just waiting it out and taking some flu medicines and fever reducers can help manage the symptoms.
Stay in bed as much as possible, get plenty of rest, drinking plenty of water, tea and other hydrating fluids and within a week to 2 weeks you should be over the influenza type A flu virus.