A Public Relation Executive can use data analysis softwares like mediametric, prezly, coverage book etc. One can get an android or ios application on play stores too.
If you are a pro R and Python are best, one can also use MS-Excel (So far, Microsoft products are evergreen ones), also Free version of Tableau provides decent options.
For sure, PR and Marketing can be integrated. It's a new market trend, blend two fields to get best out of both.
Social Media again, is an awesome tool, talk about your product, analyse opinions, comments and feedback, use analysis tools to get some useful patterns.
Hire a good content writer, and write blogs to improve product reach, let audience participate in discussion.
Public gatherings, be social, both virtually and directly ask about trends and features that people , are looking for. Analyse competition in market and innovate! Good luck!