How can I improve my face shape without the use of fillers?

The short answer is: YES. If you're not interested in fillers / fat grafting, then another option is surgery. Based on the photos and what you're saying, it appears that you have a strong mandibular angle and/or masseter muscle. Surgical contouring of the bone and midface implants may be a good option to achieve your goals. Chemical denervation (eg Botox) of the masseteric muscles is also a possibility. A thorough history and physical exam with a board certified plastic surgeon will help with selecting the best options. 

A face does not need to have a classical shape to be beautiful. In fact, most real beauty is unique, as is yours. Accordingly, I support your wish to stay away from fillers.
The  shape of a face is founded on the shape of the underlying bony skeleton. I suspect  you are concerned by the shape of your  jaw, based on the fact  you  included a close up photo of your lower face, which shows some weakness of the projection on either side of the chin, in what is termed the prejowl area. The projection can be strengthened here by placing an implant, which will provide a permanent correction. The contour improvement then provides a straight jawline, from the jaw to the chin, which is flattering. Importantly,  the soft tissues of the lower cheek above is tightened and the contouring of the neck below is improved. 
This involves surgery, but it is relatively minor and the recovery quite simple and the result permanent. Several types of implants are available, that have a long track record of safety, so individual  surgeons have different preferred implants. My preference is to use hydroxyapatite granules, which is synthetic bone of the same mineral as natural bone. The surgeon shapes this  to the individual need. As it is made of the same pure mineral as your bone,  it is  fully accepted by the body. It is porous and acts as a matrix into which your own new bone forms according to the shape created by the surgeon
Effectively it is reshaping your natural bone. 
Classically the outer cheek bone projects obliquely. Similar to the prejowl, enhancing the upper cheek tightens above and below and for improved contour that lasts and slows the rate of future ageing