If you are just on the ventolin, and are still not controlled (and it sounds as if you are not if your asthma is interferring with your sleep) then the usual thing is to start a steroid inhaler. I believe that Advair and Seretide are different brand names for the same combination of drugs (fluticasone and salmeterol) so they would work exactly the same, however most people (although obviously not everyone) is started on a steroid inhaler (so that would be the fluticasone component of the two inhalers you mentioned - although there are lots of different steroid inhalers) to see if that will control their symptoms before being started on a long-acting reliever (the salmeterol component) as well.
We cant offer medical advice on here, as we dont know you're mecical history etc. But i would go back to your GP and explain that you are struggling with your cough, and he will be able to advise you what to do.
Until you can get to your GP, you may find that sleeping slightly elevated, keeping your room as free from dust as possible, and using hypoallergenic bedding help a little, although these things are personal to everyone - if you have a look at the about asthma section on here then you'll find lists of triggers and stuff, the less triggers you are exposed to on a nighttime the more likely your lungs are to behave.
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