Does anyone here know which companies are looking for software engineers to help with this kind of stuff?
Follow press releases from company to mentioned company would be one way to start looking.
Another way would be to ask the FDA: https://www.accessdata.fda.gov/scripts/cdrh/cfdocs/cfPMN/pmn...
Searching in that form for "immunology" in the Panel field yields 500 results, and lots of companies.
That link also points to other databases.