Acetylcysteine
Acetylcysteine is a mucolytic: it breaks the disulfide bonds that hold thick mucus together, making secretions thinner and easier to clear from the airways. It is also a precursor of glutathione, the body's main detoxifying antioxidant, which is why it is used for liver support as well as for a productive cough.
It is taken with food and usually in the morning, and it works only if fluid intake is adequate — thinned mucus still has to be coughed out, and water is what keeps it moving. It should be separated from antibiotics by a couple of hours, because the two can interact in the stomach and reduce how much antibiotic is absorbed. The taste and the sulfur smell are normal for the molecule; mild stomach upset is the most common complaint.
A cough that keeps getting worse rather than looser, fever, breathlessness or wheeze after a dose, or a rash means it is time to see a doctor rather than continue on one's own.
Reference information, not medical advice. Discuss any change with your doctor.