The short answer is yes, you can do the work yourself. Some jobs can be done easily by the homeowner and do not require a recertification. Simple repair jobs like a small section of the roof (Less than 100 square feet) for example do not require inspection and recertification. A complete re-roof, new siding, replacing windows or any structural changes do require an inspection and certification before you can get windstorm insurance.
Texas Department of Insurance (TDI) maintains an excellent website that is full of information for the homeowner including a list of repairs that can be done without the need for an inspection. If you have a project that will require an inspection and recertification, I suggest you contact a TDI registered engineer prior to starting the project. This will help minimize any problems that might crop up later in the project. The more complicated the project the sooner you should talk to an engineer. Many engineers will not charge for the first consultation and advice from the outset can eliminate costly remedial work later in the project.
I have been called to look at several projects that were already well under way before the homeowner thought to engage an engineer and I have had to tell the owner that their project was not certifiable due to the way it was constructed. There are many factors that can torpedo a project. Using incorrect nails or screws, insufficient number or incorrect placement of storm ties, or incorrect anchoring of foundation are just a few of the many problems I have had to correct.
The TDI website also has an extensive list of materials they have approved for use in high wind areas and instructions for proper installation. Pay special attention to the size, quantity, and location of fasteners for proper installation as this is critical. Lastly, do not hesitate to call the TDI with questions. I have found the engineers and staff at TDI to be helpful and accessible and ready to answer questions. TDI will also provide inspections at no cost to homeowners although they are short staffed and very busy. In short, get professional qualified help and information early in your project, it will save you money and stress in the long run.