The one quart ziploc-baggie rule is for toiletries and other types of liquids, except for meds and special foods for babies/diabetics. Liquid meds do NOT have to fit in the one-quart baggie; you just have to declare them by telling TSA that you are carrying them, and offering them up for inspection.
Straight from TSA's website:
Medications
You may bring all prescription and over-the-counter medications (liquids, gels, and aerosols) including KY jelly, eye drops, and saline solution for medical purposes.
Additonal items you may bring include:
Liquids including water, juice, or liquid nutrition or gels for passengers with a disability or medical condition;
Life-support and life-sustaining liquids such as bone marrow, blood products, and transplant organs;
Items used to augment the body for medical or cosmetic reasons such as mastectomy products, prosthetic breasts, bras or shells containing gels, saline solution, or other liquids; and,
Gels or frozen liquids needed to cool disability or medically related items used by persons with disabilities or medical conditions.
You are not limited in the amount or volume of these items you may bring in your carry-on baggage. BUT if the medically necessary items exceed 3 ounces or are not contained in a one-quart, zip-top plastic bag, you MUST declare to one of our Security Officers at the checkpoint for further inspection.
The tricky issue with contacts is whether or not contact solution is a med or a toiletry. If it is a med it doesn't have to be under 3 oz., but some screeners will quibble over whether it is a medical item, so life is easiest if you can find a sample-size bottle of solution, but it is not required that you do so.