What are my rights if I was exposed to the gas fumes from a leaking stove in my apartment?

You can sue both your landlord and the manufacturer of the stove for negligence. Your lawsuit should also include a separate cause of action (claim) of strict liability against the manufacturer of the stove.  Strict liability is liability whether or not due care was exercised.

Negligence is the failure to exercise due care (that degree of care that a reasonable landlord would have exercised under the same or similar circumstances to prevent foreseeable harm).

Negligence (manufacturer of the stove) is the failure to exercise due care to produce a product that is not defective.

Prior to filing a lawsuit, it may be possible to settle the case with the insurance carriers for both the landlord and the manufacturer of the stove.

 You should notify the landlord's insurance carrier and the stove manufacturer's insurance carrier in writing that you will be filing a personal injury claim.

When you complete your medical treatment and are released by the doctor or are declared by the doctor to be permanent and stationary, which means having reached a point in your medical treatment where no further improvement is anticipated, obtain your medical bills, medical reports, and documentation of any wage loss.  Your personal injury claims filed with both insurance carriers should include these items.

Compensation for the medical bills is straight reimbursement.  The medical reports will document the nature and extent of your injury and will be used to determine compensation for pain and suffering which is an amount in addition to the medical bills.  Compensation for wage loss is straight reimbursement.

If the case is settled with both insurance carriers (landlord and stove manufacturer), NO lawsuit is filed.

If you are dissatisfied with settlement offers from the insurance carriers, reject the settlement offers and file a lawsuit for negligence against the landlord and manufacturer of the stove.  The strict liability claim is only applicable to the manufacturer of the stove.  If the case was settled with one party's insurance carrier, but not both, only name the party with whom the case has not settled as a defendant in your lawsuit.

If the case is NOT settled, your lawsuit must be filed prior to the expiration of the applicable statute of limitations or you will lose your rights forever in the matter.

First thing, before suing: get a medical opinion that a gas leak caused your health issues, because it does not matter what you are "sure" of--all that matters is what you can prove in court with medical evidence/testimony. You have to prove a link between a gas leak and your health issue to have a case.

If your health problems are due to the gas leak, get yourself a personal injury attorney, who can evaluate your case and advise you on your options, including what to sue. To oversimplify, if the stove was manufactured or designed incorrectly, you sue the manufacturer; if the stove itself was fine, you sue the person or company who installed, which is presumably the complex (if their staff installed it).