Just an asthma cough?

[AccidentallyRunToWindsor]

Since about yesterday afternoon I have been wheezing with various degrees of severity, have been able to control it with ventolin so nothing to worry about.

However I started with a cough last night, very dry much like a cough I would get with asthma, it's woken me up with it just now. I had a sore throat for a day in the week but my temperature is still low (35°)

I don't want to waste 111's time but am not really sure if this is just asthma or not.

I can't say for sure. But it could be CV so best to treat as if it is. My DD2 has had CV and although she had a high fever for 4 days, she also has a cough. She described it as "fluffy, tickly" throat and it felt "tight". She also has mild asthma but this felt additional.
We've found that dampening the air helps: a wet towel hung next to your bed may do the trick. HTH