From a US point of view, the answer is "maybe" leaning towards "probably not."
Generally, the liability of the product will fall upon your employer. Assuming that you're not an owner of the firm, you would not be participant in the (vast) majority of any potential lawsuits.
The exception to this is gross negligence. (Un)Fortunately, gross negligence can be a highly subjective term, and can be equally difficult to prove in court. Every software product has some degree of problems with it. So long as there are some recorded(!) Test and QA activities that cover the majority of mainline function, the risk of being successfully hit with gross negligence is fairly low. It's important to keep records as they'll carry a lot more weight during a trial.
No one tests everything, nor is it even possible, so don't take the above as grounds for assuming anything less than 100% code coverage as not acceptable. Given that it's a medical product where lives and / or health could be affected, your burden is a little higher. OTOH, the product isn't prescribing the actual dosage to be taken so the burden isn't as high as it could be.
While the product can be released under the not-for-profit's name, that doesn't absolve your employer from liability. Even if the NFP has signed documentation indicating they accept liability for the product, they can turn around and claim that the requirements or testing were insufficient and drag your employer into any potential lawsuit. Ultimately, the company that made the product will always have some degree of liability for the product.
If you happen to be a licensed / professional engineer, which I doubt since you would have mentioned it, then you have a higher standard to hold yourself to. If you are a PE, you may personally be held responsible for some of the product's shortcomings if you failed to adhere to reasonable development methodologies. This is especially true if you are expected to stamp / seal the design or implementation documentation. That having been said, you would have already been aware of your liabilities as a PE if you were one.
Legal liability is one thing, moral liability is another. You need to be able to sleep at night knowing that the product you were working on didn't have any gross flaws that could significantly affect someone's health. It's also important to keep the product in perspective. This is likely a reminder / helper type system. It does not abdicate someone's own personal responsibility in maintaining their health. Do your best to make sure the product is solid, but also keep the ramifications of a bug in proper perspective.