SYDNEY, Jan 4 (Reuters) - Australia"s COVID-19 cases touched a fresh pandemic high on Tuesday amid an Omicron surge in its two most populous states as hospitalisations in New South Wales (NSW), home to Sydney, surpassed the record numbers hit during the Delta outbreak. NSW and Victoria, home to more than half of Australia"s 25 million people, saw another spike in infections, with 37,151 new cases reported between them, just shy of the national one-day high of 37,212 hit a day earlier. Tasmania reported 702 new cases. Other states and territories are due to report their numbers later in the day. People admitted in NSW hospitals rose to 1,344, a new pandemic peak, topping the 1,266 reached last September during the Delta wave. Numbers have more than doubled in a week, straining the health system. Authorities are also battling a shortage of rapid antigen tests, delays with PCR results and the abrupt closures of a number of testing sites as Prime Minister Scott Morrison ruled out the government covering the cost for people to test themselves for COVID-19. read more "The problem at the moment is that the lack of (rapid antigen tests) is completely hampering personal responsibility and it is a frustration that is a glaring hole in the current management of COVID," Chris Moy, vice president of the Australian Medical Association, told ABC Radio on Tuesday. The record spike in infections and hospitalisations have come as 2 million more Australians became eligible for their COVID-19 booster shots from Tuesday after authorities shortened the wait time between second and third shots to four months. Just over 2.5 million Australians have so far received their booster shot, which health officials are betting may prevent more hospitalisations and deaths. Australia on Tuesday crossed half a million coronavirus cases since the pandemic began, with about 94% detected since last July when its east was rocked by a Delta outbreak. Still, the country"s near 538,000 cases and 2,270 deaths are lower than numbers seen in many comparable countries.