This sounds exactly like asthma to me. Go back to the Gp and see a different one preferably. Tell them you have alot of astma in the family (even if it's not actually true) and could you please have a peak flo meter to start analysing her lung function. Normally you do this 3 times a day. After about 2-3 weeks of daily readings, you go back to the doctor and it should show a variability in lung function if asthma is present. If you still get no joy ask to be referred to the hospital pead and explain that it is affecting her behaviour, sleep etc etc. Sometmes you just have to go back and not leave till you get what you need.
Keep on with the anti histimine also. You sometimes have to be taking this for a while before it starts to make a difference. Also don't stop taking it when the pollen count is low, it might not only be pollen she is allergic too, it could be many things. Also try a dairy free diet and cut wheat and gluten too. These are known triggers for bronchial dysfunction. illiminate as many soft furnishings also, turn curtains into blinds, take teddies out etc and put mattress/pillow protectors on the bed. Also, raise the head of the bed as this might help too.