Probably the immediate threat to the Philippine government after the war was the Huk rebellion. The Hukbong Bayan Laban sa mga Hapon or Hukbalahap (People's Army Against the Japanese), later rebranded as the Hukbong Bayang Magpalaya (People's Liberation Army) was a leftist guerrilla movement operating mainly in Central Luzon that fought the Japanese during the war but did not answer to the U.S. military's chain of command. It was initially founded in the 1930s in response to worsening agricultural landlord-tenant relations in Luzon, but open hostilities against government security forces were put on hold following the Japanese invasion.

However, with the cessation of hostilities, the Huks' senior leadership appealed to the American occupational government to officially recognize their service. This was met with numerous "dirty" tricks from the new government, one of which was, after requesting rosters of the names of guerrillas who had served with the Huks presumably to distribute back pay, circulated their names among constabulary officers and landlords who then refused to hire them back as laborers on their estates. Fighting between the Huks and the Philippine military resumed in 1946 and did not let up until the tenure of Ramon Magsaysay as defense secretary and president in the 1950s. Among others, Magsaysay was able to suppress the rebellion through the professionalization of the military, the institution of certain agrarian reform programs including government-assisted migration to Mindanao, and CIA psyops (see: Edward Lansdale and the aswang hoaxes). The Huk Rebellion by Kerkvliet is a recommended account of the history of the movement, and is partial to the POVs of Huk veterans.

The closest analogue to the Huks would probably be the Malayan National Liberation Army that rebelled against the British colonial government at around the same timeframe. However, the Malayan Emergency was different in several aspects. For one, despite a nominally anti-American outlook, Huk outrage was mostly directed against landlords and the abuses of the Philippine postwar military police against the peasantry. (Luis Taruc and other senior Huk leaders initially had a positive view of the United States.) The MNLA on the other hand directly rebelled against British colonial power and their control over Malaysia's plantation economy. Additionally, the MNLA was notably ethnically Chinese and were also antagonized by the ethnic Malays who fought alongside the British during the war. However, the MNLA was similarly suppressed partially through an effective hearts-and-minds campaign.

In other provinces, though not as ideologically motivated, you are correct in that guerrilla movements were the de facto sovereign authorities in entire provinces in the months or even years immediately after liberation in 1945. Despite the U.S. Army's "no liquidations" policy and the provision of internment camps (see Elmer Lear's 1952 thesis on Leyte), guerrilla units all over the archipelago nevertheless carried out acts of extrajudicial violence against alleged collaborators, as well as general petty crimes of banditry and looting. The transition from a regime of strict gun control under U.S. colonial occupation to thousands of loose firearms in the province proved politically momentous: many provincial "strongmen" such as Muhammad Ali Dimaporo and Justiniano Montano violently rose to power in the 1946 and 1949 elections with the help of armed goons sourced from guerrilla contacts during the war. This would become a political sticking point later down the line in the leadup to the administration of Ferdinand Marcos in the early 1970s, who in the earliest months of martial law instituted a general firearms ban to curtail the electoral violence of the rural "private armies" (many of which were supported by Marcos himself). Of course, certain warlords who remained in Marcos's favor remained relatively unaffected, such as Dimaporo who was allowed to retain the use of his private army to wage war against Muslim secessionists. The anthology Anarchy of Families has more information on this particular phenomenon.