T.F.
It really sounds like you're on a good course of action and are using good judgement about the drugs. Great that you're trying to solve the physical problem and not just rely on drugs. They definitely have their place as pain can be so debilitating.
Other things you might consider....Is your posture when you work on the computer what it should be? Are you getting up every 20 minutes or so and stretching? Do you walk the dog or carry it? Could you be doing this in a way that irritates your spine? Carrying your 23 month old, putting her in and out of the car, stroller, holding her hand while she's walking, can really do a number on the spine. It takes awhile to train/strengthen the muscles to support your spine and not let things slip, causing the pinched nerve again. The physical therapist should be able to give you specific stretches and exercises to strengthen the problem areas and make sure to think through the above so you can inform the PT of how you move and what stresses you may be putting on your back/spine/neck. They may also have some ideas of better ways to do some of these everyday things.
Ask your doctors what kind of timeline they see as far as improvement. Then you will know what to expect. It may be that you'll have to be extra patient if the problem is lugging a 2 year old around and learning creative ways to do that without putting as much stain on your body. This could be different from someone who hurts themselves in an accident that doesn't occur everyday. They would have a better chance of letting things heal and settle.
If you think you've been misdiagnosed, ask for a second opinion or if you're feeling like you're not getting what you should from your chiropractor, PT or any doctor try someone else. It's not always an issue of "fault" or the qualifications of the doctor. My husband is a chiropractor and there are different methods of chiropractic. He's had patients referred to him from other Chiropractors because the patient wasn't responding to a specific method and visa versa. It doesn't happen often but it does. All the Best to you!