Is there a way to search for more recent papers than the one I'm currently reading?
A simple way that I usually follow to find newer papers about the same topic is using google scholar. Google scholar gives you the ability to find papers that cited the paper you are interested in, and those papers are usually published after the paper you are interest in has been published (i.e. more recent work).
For the example you provided in your comment, google scholar gives me 57 articles/results that cited your example
In addition to Google Scholar, you can also use Web of Science. For the article you gave, some keywords would be "Postpartum psychiatric disorder" and "pregnancy". You can search Web of Science for papers on this topic, i.e. any paper with all four words in the abstract and / or the title.
You can refine the timespan (2013 to 2018 for example), search for the complete phrase (enclose the phrase with inverted commas), search for individual authors, and so on. After performing the search, you'll reach a screen where the left-hand column lets you further refine the results, e.g. by excluding all social science papers. As of time of writing there were 1607 papers matching this search (I clearly used overly general search terms).
Web of Science is more exclusive than Google Scholar - it indexes only journals that have SCI impact factors, while Google Scholar indexes everything. Google Scholar is also free while Web of Science isn't (however if you are affiliated with a university, chances are very good your university library has access). Which to use is up to your requirements.
If have some time for a non-simple way, you can datamine arxiv with this tool.