Unfortunately I have not seen any TV ads here, selling medicines. However, if I am given specific symptoms I can sometimes suggest a rule-of-thumb popular remedy. The more symptoms and details the remedy is based on, the more likely it is to work.
Homeopaths generally do not prescribe palliatives, as they try to find and cure the underlying causes instead. For instance, a Homeopath might rather not suggest a pain-killer for headaches, as this might conceal the real cause which can become worse. The difficulty in suggesting remedies online, is that symptoms given are usually very generalised and limited in number. In Western culture, we have a tendency to talk about, for instance, a headache. My Kent's Homeopathic Repertory has 90 double pages of discussion on various headaches. A good Homeopath would collect many more symptoms than simply a headache, and would need details of the headache too, when did it start, where is it, what eases it or makes it worse, is it lancinating, is it dull, does it throb, is there nausea, is it associated with other pains and symptoms, does eating affect it, what light does the patient work in, how is the patient's digestive system, are there eye problems, stress factors and dozens more.
However, there are certain acute situations which are easier to treat, and which only require a little sleuthing. So, yes, sometimes I can suggest good remedies based on very little information.