There needs to be a distinction established between the "late Ptolemaic" army and what was going on by the time of Caesar's arrival in 48.

The Ptolemies maintained a traditional Hellenistic (Macedonian) army from the get-go, with massed phalanx formations and default use of the sarissa, a very long pike. They carried round shields (rather small on the whole, due to the size of the sarissa) and were supported by auxiliary cavalry. They were at the core infantry-based armies, but with heavy use of cavalry (and even elephants) in the legacy of Philip's reforms. There were some skirmishers which carried lighter armaments, depending on the area.

By the time Caesar arrived, this basic Macedonian type had been heavily modified in Egypt. Roman mercenaries had been present in the Ptolemaic court since the 3rd century, and their influence was marked. The army came to be organized around new leader type called a hekatontarch, or leader of 100. These were functionally very similar to a Roman-style centurion. There is also a gradual introduction of Roman infantry equipment, with the theuros (oblong "door") shield appearing along with swords similar (or even identical) to the Roman gladius and longer Celtic types. We also hear about a new command unit called the syntagma which included such ancillaries as a standard-bearer. To these Roman influences must be added Celtic influences from the Galatian invasion of Asia Minor. In addition to the gradual shift of the army structure and equipment and the direct infusion of Roman adventurers/mercenaries into the ranks, there were the famous Gabiani, Roman legionnaires who had been left in Egypt by Aulus Gabinius in 60 BCE (he was governor in nearby Syria and had been meddling in Egypt's near-constant dynastic tiffs). These soldiers formed a core of a new hodgepodge of Macedonian, Roman, Greek, Gallic, German, Egyptian, and other elements. The Gabiani married Egyptian gals and many remained permanently.

So by the time of Caesar's arrival, the Egyptian army was a core of "Macedonian" or "Hellenistic" infantry, some formations probably still with sarissa but others now using the more flexible sword and oblong shield, and certainly using the more flexible system of 100-man units. Added to this core were the Gabiani, who fought more or less the same as any Roman legion and probably added to their ranks non-Romans whom they had trained, either Macedonians or others. There was cavalry, of course, like all Hellenistic armies, drawn from whatever sources were available. And surrounding all that, mercenary groups of all flavors and sizes.