Did temperature for the US state of Illinois reach an all-time record low 1/31/2019?
The record is unlikely to change, at least based on the particular measurements provided in the initial question.

According to the Illinois State Climatologist Office at the link you provided, the -37°F temperature record was discarded for lack of quality assurance: "However, that observation came from a small airport station designed for aviation purposes and was not part of the climate network in Illinois. As a result, the data were not always archived and no quality control procedures were applied to the data."

From the URLs in your question, the recent weather observations you refer to exist within Weather Underground's network of personal weather stations. In other words, they are often relatively inexpensive sensors that are owned and maintained by private individuals, and their measurements will not have the accuracy required to be included in the official temperature records for the state. The actual temperature at the Sinnissippi Point station may or may not have been colder than Illinois' verified lowest temperature, but without additional info (e.g. knowledge of specific instruments/sites and operator, as implied in the answer by @DavePhD) the official record will not change based on that measurement.