How should I determine patentability and possible monetization of my work as a researcher?

Your question raises several issues.
1. Patentability
Patents are national rights, and the exact requirements for patentability vary from country to country, but at the very least the invention must be novel and non-obvious. You state that you have not seen any publication of similar work, which is encouraging. It would be a good idea to carry out an internet search of both journal publications and patent applications to see if any relevant publications exist. Patent databases can be searched for free, e.g. http://worldwide.espacenet.com/
Please bear in mind that your own publications (written or oral) may affect the patentability of your invention. In some countries such as the US there is a 12 months grace period in respect of the inventor's own disclosures, but in some other countries no grace periods exist in this regard.
A patent attorney can also advise you regarding the patentability of your invention, in particular as to whether your invention falls within one of the exclusions from patentability.
2. Ownership of the invention
I would suggest that you check with the university what their standard terms and conditions are regarding the ownership of intellectual property generated by PhD students. You indicate that you developed the method during your PhD, but that this research was not part of the work that the university had hired you to do. However, the assessment as to whether a particular invention forms part of someone's job or PhD duties is typically not straightforward and would have to e assessed by someone in possession of all of the relevant facts.
You should also clarify whether the PhD was funded by a party that might have rights to any of the IP, and whether any collaborators or colleagues were involved in the project.