Both states existed for a long time, so there's not going to be a simple answer. I do know that, re: the early period of Carthage, Richard Miles mentions definitively that Carthage did have an important trade relationship with Egypt -- this was to illustrate the independence of the colony from the mother city, as Tyre was under pressure from the Assyrians to embargo trade, but Carthage stepped into that trade vacuum.

As already mentioned, while both states are in North Africa, they're quite far apart; still, Ptolemaic Egypt extended control to Cyrene, and there were Carthaginian satellites quite far east along the Syrtes, so the two powers were more or less neighbours and must have had some degree of understanding over the frontier space, but this wasn't a particularly developed area. We also work with the difficulty that Carthaginian sources are practically nonexistent; Egypt is well-covered, though, so there may be some evidence on that side of any particulars to the relationship.

To my knowledge of the existing record, there were never any wars or alliances between the Ptolemaic kings and Carthage. Carthage wasn't adverse to allying itself with foreign kingdoms, they conspired with the Macedonians against Rome during the second Punic War. And there would have been quite a bit of trade between Egypt and Carthage, so they would have come into contact. That said they were quite far apart (~2600km between Alexandria and Carthage) and they didn't share major rivals, in fact during the time that Carthage was a major power (before the second Punic War) Rome similarly had few dealings with the Ptolemies.