Please be very watchful and careful with "coughs". It is possible to have "walking pneumonia" -to be quite seriously ill, and not realise it.
As a good rule of thumb, if there's any fever which continues with the cough, it's best to visit a doctor.
There are herbs which would help with this, or any cough. But it's wise to get a diagnosis first.
Immune herbs such as Echinacea angustifolia, Astragalus, and Androgaphis.
And symptomatic herbs such as Angelica root, coltsfoot, mouse ear, liquorice....etc.
But before trying any herbs check that they are suitable for you to take, as it is possible for allergic reactions to occur, or to take the wrong herb (a cough suppressant, for example, when coughing up phlegm is advised.)...or to have a pre-existing condition when a certain herb is inadvisable.
A qualified medical herbalist would help.