There are several things you can do that may help with your cough.
Bronchoforce is traditionally used for chesty coughs and I would also suggest a probiotic.
Unfortunately, antibiotics tend to kill off the friendly bacteria in the gut which are very important for immune support.
Killing them off can weaken your immune system which in turn can leave you more vulnerable to repeat infections.
You should be able to get a good probiotic from your healthshop. Just let them know it is for after antibiotic use.
I would also reduce your intake of dairy products as these can be very mucus forming and can contribute to the problem.
Make sure, too, that you are drinking plenty of plain water every day as dehydration may make symptoms worse.