The PCR-test is the best test we currently have to test the population in a useful and generally reliable way.
While it is true that the test can remain positive after a few weeks after the infection or onset of symptoms, the percentage is close to 0 after about 6 weeks. [1]
So as it's the end of April, the January infections will not have any false-positive influence on the current wave.
[1] https://academic.oup.com/cid/article/71/16/2249/5822175