Iapyx is the son of Daedalus, brother to Icarus. Apollo gave him the gift of healing and was with Aeneas as a hand-full of Trojans fled the fallen city. What more is known between/after these snippets of info. Specifically, where was Iapyx when Daedalus and Icarus were trapped in the tower by Tyrant Minos?
Iapyx the son of Daedalus is a different character from the physician compatriot of Aeneas. For some reason certain translators, especially in previous centuries, render the name of Aeneas's companion into English as
Iapis (e.g. John Dryden's 1697 translation of Virgil's Æneid; William Smith's 1867 Dictionary of Greek and Roman Biography and Mythology; & Carlos Parada's Greek Mythology Link website).
It is Strabo in his Geography (6.3.3) who claims that Iapyx "is said to have been the son of Daedalus by a Cretan woman and to have been the leader of the Cretans." A bit further into the same chapter it is mentioned that a colony was set up in the Italian city of Brentesion, called Brundusium in Latin, "by those who set sail from Sicily with Iapyx... although they did not stay together there, it is said, but went off to Bottiaea", a region of Macedonia. Strabo then never mentions this Iapyx character again, so we know nothing of his interactions with his parents or with his brother Icarus.
The implication is that Iapyx was born on Crete Island and at some point in his life led a migration of his fellow Cretans to Italy, where he became the ancestor or first ruler of the Iapyges, a group of tribes inhabiting the Apulia region in ancient times, and whose territory was thus called Iapygia. Every other Iapyx in Greco-Roman mythology is basically a device to explain the origin of these Iapyges. The one exception to this is a Theban who is brutally wounded by Theseus in Statius' Thebaid. This is the only thing that Statius tells us about him.
Another Iapyx, who lived centuries before the Trojan War, around the time of Deucalion's Flood, was one of the fifty sons of King Lycaon of Pelasgia (later called Arcadia). He moved from Pelasgia to Italy with two of his brothers, together with whom he is alternately called the eponymous ancestor of the Iapyges. In another version this ancestor is a son of Apollo by a Lycian nymph, and said to have been the brother of Icadius (or Eicadius) and Patarus.
Aeneas's doctor Iapis/Iapyx is a character from the 12th and last book of Virgil's Æneid. Aeneas calls him
Iasides, "[Son] Of Iasus." This Iasus was dying at the time that Apollo approached Iapis, wishing to grant him the gifts of prophecy, skill in playing the lyre, and powerful archery. Wishing to prolong Iasus' life, however, Iapis "chose knowledge of the virtues of herbs, and the use of medicine, and, without fame, to practise the silent arts."
The only other scene in which Iapis appears is narrated immediately after that back-story. Iapis is now an old man and Aeneas is wounded, the arrow with which he has been shot now stuck in his flesh. Iapis tries to heal Aeneas using Apollo's drugs but fails. Aeneas' mother the goddess Venus intervenes and with her surreptitious assistance Iapis is able to easily remove the arrow and heal Aeneas. The doctor then admits to his patient:
"Aeneas, this cure does not come by human aid, nor guiding art, it is not my hand that saved you: a god, a greater one, worked this, and sends you out again to glorious deeds."
We do not hear of Iapis again, although, considering his geographical location, we are presumably intended to connect him with the Iapyges in Apulia.
Earlier in the Æneid, in Book 5, Virgil refers to Aeneas's steersman Palinurus as
Iaside, "[Son] Of Iasus". Based on this, Carlos Parada, on his Greek Mythology Link website, concludes that Palinurus and Iapis are brothers, sons of the same Iasus.
Assuming that Iapis is not merely a different rendition of Iapyx the son of Daedalus, then it is possible that both men—Iapis and the Cretan Iapyx— were present at Troy during the Trojan War, Iapis on the side of the Trojans; Iapyx within the Cretan ranks among the Greeks. However, no such details are mentioned by Virgil or Strabo.
All Æneid quotations are from the translation of Virgil on A.S. Kline's Poetry in Translation website.