The test is not so easy as it might seem, and Adobe Reader commonly gets it wrong.
The simple test is to look for the AcroForm key in the root object, then see if it contains a non-zero list of fields. This still doesn't prove it is fillable, because it could be just navigation via buttons (which might not look like buttons). There are also he entirely separate class of XFA forms.
You cannot analyse a PDF reliably by searching for strings, not least because a PDF may still contain deleted objects. You need a true PDF parser, which uses byte offsets in the xref tables and works through a heirarchical tree of objects.
You will certainly need to spend some time reading the PDF specification, even if you use a parsing library.