In recent years, social media has been criticized for yielding polarization. Identifying emerging disagreements and growing polarization is important for journalists to create alerts and provide more balanced coverage. While recent studies have shown the existence of polarization on social media, they primarily focused on limited topics such as politics with a large volume of data collected in the long term, especially over months or years. While these findings are helpful, they are too late to create an alert immediately. To address this gap, we develop a domain-agnostic mining method to identify polarized topics on Twitter in a short-term period, namely 12 hours. As a result, we find that daily Japanese news-related topics in early 2022 were polarized by 31.6\% within a 12-hour range. We also analyzed that they tend to construct information diffusion networks with a relatively high average degree, and half of the tweets are created by a relatively small number of people. However, it is very costly and impractical to collect a large volume of tweets daily on many topics and monitor the polarization due to the limitations of the Twitter API. To make it more cost-efficient, we also develop a prediction method using machine learning techniques to estimate the polarization level using randomly collected tweets leveraging the network information. Extensive experiments show a significant saving in collection costs compared to baseline methods. In particular, our approach achieves F-score of 0.85, requiring 4,000 tweets, 4x savings than the baseline. To the best of our knowledge, our work is the first to predict the polarization level of the topics with low-resource tweets. Our findings have profound implications for the news media, allowing journalists to detect and disseminate polarizing information quickly and efficiently.