You don't go to a formal hearing until you've spoken with a protest official, which you do in person. If you do not get the results you want there, then you get a hearing. You really do not need sworn testimony. Just do some research on the property values in your neighborhood on the HCAD website, get the average $/per square foot, year built, etc., put them in a chart or table, showing how your appraisal is different than that of comparable houses. If a house in your neighborhood skews the averages (and makes your comparison unfavorable), find out why and take a picture of the house. For example, we bought in an older inner-loop neighborhood and most of the property values are consistent. However, there are a few teardowns with new big homes, which were valued much higher than the rest of the neighborhood, and made our value look comparable. I took a picture of the new house to show that my older house should not have the same value as the new house. Also, take a picture of every imperfection in and around the house -- cracked driveway, drywall cracks, etc. That's all you need. The informal meeting will typically take care of your protest unless you want something outrageous.
If you really want an affidavit, prepare it (you can probably get a form online), all but the signature, and find a notary public.