Betta Choking On Hair Algae

Hi,
 Last night my betta accidentally ate some of the hair algae in my tank and was choking horribly, and she hasn't been able to get it out of her mouth since. It's hanging out of her mouth and bothering her. 
 
 What should I do??? I tried to pull it out with my fingers, but it's kind of small. I have a couple pictures.
 

Thanks for the reply! 
  Someone told me If I pulled it out, I may pull out her stomach etc.  So far she's just been trying to spit it out every now and then, other than that it doesn't bother her too much. I think I'll just have to let her figure it out.

P.S Any tips on getting rid of the hair algae? I've been battling with it for ages.   

I've just realised my post sounded like I was suggesting to pull the algae out of the fish, I meant to pull it out of the tank, sorry for not making that clear 

I found I couldn't get rid of it by curing the cause, I used to spend quite a while winding it round my finger to physically remove it from the tank. But it recently seems to have vanished of its own accord. (Touch wood!) The only thing that's changed is I've got more live plants and got rid of the fake ones. Maybe the plan experts could say if that's cause and effect or just plain coincidence.