How to know if this is a chest infection or my asthma?

Several things: Asthma is not a respiratory infection. Infections often- but not always) can be easily diagnosed with blood tests, chest xrays and other symptoms that a physician can make the diagnosis. Asthma is not an infection and its symptoms are not always the same as an infection.

Fever: Often a chest infection (pneumonia) will also present with fever (not always), so that may be a factor that differentiates the two. It is always good to talk to physician who will examine you.