Your summary might be framed this way.
I was handed a set of samples by a colleague. I characterized the samples in a specialized instrument, analyzed the data, and generated a report on the results. The only inputs that were given to me were the samples and the types of results desired. I worked independently using these inputs and turned over the report at the end. I did not consult with the colleague to decide why certain approaches in the characterization and analysis should or should not be taken. I did not enter into discussions about the interpretation of the results within themselves or in context to other findings from my colleague. Can I now claim right to co-authorship on a publication that includes the results from my report?
In the above frame, the most direct answer is no. First, the hard reason. You did not negotiate a contract on your duties and rewards before the fact. The party that got your report is under no a priori contractual (legal) obligation to award you co-authorship. Not simply written, not even verbal. This is not a happy situation to reach. As might be said also by others, at best, this finding can serve you as a lesson for next time.
The second reason for an answer "no" concerns the answer to the question of whether your colleague has any ethical responsibilities to include you as co-author. As you briefly framed your case, and as I have reframed it in greater detail, you served primarily if not exclusively as a service provider for the work done. You took in samples, took in a description of what was desired as the output, ran a specialized instrument over the samples, and provided the desired output result using the given inputs. Some consider the level of work just described as not being worthy of co-authorship on a publication. Some will instead consider it more responsible to be recognized only in the acknowledgement section of the publication.
The extent that the work you did deviated from the above description must be considered. Did you provide "original ideas" during your discussions, for example by suggesting different approaches to the characterization or analysis to obtain results that provided greater insights in their own right or in the larger context to the entire work itself. In addition, you will have to consider the extent that the other party carries your same ethics about co-authorship roles and perhaps even the extent that the journal enforces standards on when to acknowledge contributors to its publications. All these factors, which you have left rather unclear in your post, will dictate how much room you may have to negotiate for co-authorship or acknowledgement on the paper. If you do go down this path, you will benefit by having someone with a deeper background in your case to advise you on the best professional approach to take. Ultimately, you may find the effort so overwhelming that you simply have to allow even this level to pass as a lesson this time.
In summary, given that you have no a priori contract, and presuming that the ethical frame does not deviate significantly from the above, you may face insurmountable hurdles in pushing any further for co-authorship. At best, you should ask for recognition in the acknowledgement section. You should certainly do so in consultation with someone who has insights and experience to support your case. Finally, the scale to define what level of involvement leads to what reward in a publication, from being left off to being acknowledged to being a co-author, is not linear, standardized, or always agreed-upon by all parties involved. You likely have some further discovery to make beyond asking here for an affirmation.
Finally, with regards to the last part about discovery and consultation, implicitly understood in your posting is that you are working with a (different) PI. What advice does your PI give you about this situation? Was your PI in agreement with your decision to do characterization and analysis work for someone on a different project and then simply hand out the results from that work without some up-front agreement? What does your PI say to your attempts now to try to take back or block those results from publication? Your next step should be to answer these questions and follow the commensurate advice from you PI.