The leading remedies on my repetorization are, in order of indication by this method: arsenicum, hepar sulph, mercurius and sulphur. Arsenicum, lycopodium and sulphur appeared in all six rubrics chosen.
Other remedies which placed well in the repetorization are: graphite (not in fissured tongue or swallowing pain), kali bichromium (not in irritability), lycopodium, nitric acid (not in irrit and swallowing pain), and phosphorus (not in cracked face or swallowing pain). I'm also curious about arum triphyllum because it keeps coming up in class as being characterized by cracking. I wanted to find a suitable rubric for the dryness that would include the fact that there is no exudate on the tonsils, but have not yet found such a rubric. Dryness of the other parts is incorporated into the concept of the cracked rubrics, as tissues do not often crack if they are not both irritated and dry. I'm also already up to six rubrics, which is one more than I intended to use at the outset.
The only materia medicas that I have at home are Phatak and Morrison, and I used both of them heavily to read up on these remedies.
The remedy that is most strongly indicated is arsenicum. One might argue that there are no ulcerations, that there is no sign that the child is better when warm, or that the tongue is not coated. But the case is acute and brand new, and with so many of the boy's parts cracking open, ulceration is in his near future. He has a fever and pretty much everybody who has a fever is better when warm. And just because a tongue coating is not mentioned in a written case doesn't mean that it is not present, or about to appear. Arsenicum experiences cracking, is irritable and phobophobic, has trouble swallowing, has a fissured tongue and dripping discharge. In this case the discharge has caused severe irritation of the skin between the nose and lips, and the discharge might be considered "excoriating", which would be another indication for arsenicum.
Arum triphyllum kept coming to mind even though it didn't rise to the top in my repetorization, because it is mentioned with cracking. According to Phatak it has acrid discharges with sore/raw/burning parts, mouth breathing and flowing coryza, and cracked lips. The description matches very well, but relative to other remedies Phatak doesn't have much to say about this remedy and it is not represented in Morrison for pharyngitis at all. At this point I consider this remedy to be a close second to Arsenicum and will seek out more information about it.
Hepar sulph scored well but is not a suitable match because the case is brand new, not advanced, and not suppurative. There was no mention of the pain radiating to the ear or peritonsilar abscess, and though we can assume that a feverish patient is likely to be better warm worse cold, it was not given as a strong modality.
Lycopodium is predominantly right sided, at least at the beginning, and worse in the afternoon, but these symptoms are not present in this case. It also does not appear that the child is weak because of malabsorption, or that the symptoms are repeating or alternating. The mouth breathing fits, but the tongue sx do not match. Overall Lyc is not even close.
Mercurius is tempting but as with Hep sulph the severity does not match. Also in mercurius we would expect to hear about night sweats, foul breath or bad taste in mouth, salivation instead of nasal drainage, and imprints on the tongue instead of fissures just back from the tip.
Sulphur may well be the solution, but the picture is not clearly sulphur. The burning and rawness of the throat are a match, as are the chapped lips. However the child is averse to bright outdoor light, not warm rooms. Sulphur usually wants cold drinks, but according to Morrison wants warm drinks when it has a sore throat. That craving is also not mentioned in this case.
I had to look up Nitric Acid because of the excoriating nature of the nasal discharge and the fact that so many parts of the face are cracked. Nit ac has trouble swallowing and has cracks at mouth corners or possibly on the tongue, and this child has both. With Nit-ac we would expect dark red tonsils that are indurated or ulcerated, but the case only mentions redness which would be expected in general with a strep throat infection. Again the bad breath and stinky sweat are absent. The irritability is certainly a good indication for this remedy also.
I also looked up Lachesis though it didn't score well on my repetorization. It scored better on a previous attempt, and because of the locations of the tongue fissures it kept coming to mind. Not a split tongue, but a tongue with the tip separated by fissures from the rest....lingered on my mind. But the boy's problem is not localized to the left, and there is no sense of constriction at the throat, so it is just a thought, probably not indicated in the least.