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There are a few things that can cause this. Holly scorch is the most common. This happens when the weather changes too quickly. The plant will recover from this on its own.

Here is an article that you may find helpful: https://www.gardeningknowhow.com/ornamental/shrubs/holly/trimming-holly-bushes-how-to-prune-holly-bushes.htm

There are several diseases it could be. I would check the roots first. You may have a root rot that is slowly killing the roots and eventually the leaves. Some of the root rots can be treated by drenching the soil with fungicide, but some cannot be treated and the plants need to be removed. This is the most likely cause. Root rots tend to occur in plants that are in soils that have drainage problems and will return if the drainage is not improved.

Also, check the stems. There is also a possibility that it is a canker that is affecting the plant. This is less likely, but possible. Cankers can be corrected by treating the plants every few weeks, for a few months, with a fungicide. Cankers will likely be lower down on the affected limbs and will look like sunken spots on the wood.

It sounds like your holly has developed a condition called witches broom. In warmer climates like yours, it is typically caused by Sphaeropsis tumefaciens.

This article on it should help:
https://www.gardeningknowhow.com/ornamental/trees/tgen/witches-broom-disease.htm

A Dwarf Burford Holly grows 6 to 8 feet high.

Gardening Know How provides gardening advice, not plants. I would recommend you make an inquiry at your local gardening center about purchasing one.

For more information on the care of holly bushes, please visit the following link:
https://www.gardeningknowhow.com/ornamental/shrubs/holly/growing-holly-bushes.htm

Holly have a tap root and an extensive lateral root system.

They will send up shoots from this lateral root system.

There is little to be done except remove the shoots as soon as possible. Cutting down into the roots with a sharp shovel may cut the root system more sharply and reduce them from growing back as quickly.

You can try adding some water to the plant and adding 2 to 3 inches of mulch to aide in moisture retention.