how to remove cold and cough

Use honey. Honey is an effective way to suppress a cough and soothe a sore throat.[2] Several studies have found that honey is at least as effective at reducing cough than over-the-counter drugs, and is sometimes more effective.[3][4] Honey helps coat and soothe mucus membranes. It can be very helpful right before going to bed if the cough is making it hard to sleep.

It's good for adults and children, but do not give honey to children under the age of 1 since it could increase the risk of infant botulism.[5]
You can take the honey directly. Try 1 tablespoon every few hours while your cough persists. Another option is to add 1 tablespoon or more to a glass of warm tea with lemon.
Some studies suggest that honey is as effective as a cough suppressant as dextromethorphan, an ingredient commonly used in many over-the-counter cough suppressants.

Drink licorice root tea. Licorice root tea soothes your airways, helps ease inflammation, and loosens mucus. To make it, place 2 tablespoons of dried licorice root in a mug and pour 8 ounces of boiling water into the mug. Steep for 10-15 minutes. Drink twice daily.[7]

Don't drink licorice root tea if you are on steroids or have kidney problems.
The active ingredient, glycyrrhiza, can cause negative side effects for some people. Look for DGL, or deglycyrrhizinated licorice, at your health food or drug store. It is just as effective

Try thyme tea. Thyme is used in some countries, like Germany, for a variety of respiratory ailments. Thyme helps relax throat muscles and reduce inflammation. Boil water and place the water and 2 teaspoons of crushed thyme in a cup for 10 minutes. Strain before drinking.[9]

Add honey and lemon for extra soothing properties. It may also help make the taste more pleasant.
Do not use thyme oil internally. Use dried or fresh thyme

Enjoy a piece of hard candy. If you do not have any cough drops on hand or would prefer to stay away from medicated lozenges, you can usually soothe and stop a cough by sucking on a piece of hard candy.[10]

A dry cough that produces no phlegm can be halted by nearly any piece of hard candy. Hard candy causes you to produce more saliva and to swallow more, thereby suppressing your cough.
If you have a wet cough that does produce phlegm, lemon drops tend to work well.[11]
Hard candy is an effective cough remedy for children ages 6 and older.[12] Don't give hard candy or lozenges to children under 3, as they could choke