The law determines the legal process for assessing property taxes and it varies widely from one state to another. It all depends on property tax statute in your state, and how property taxes are calculated under said statute. Some states calculate based on price paid and year acquired, while others periodically re-assess every property based on current market value.
You can likely sue only if you can prove that the county is not following the law in how they are taxing you. Alternatively, in many states there is a legal protest available to property owners. You can try that process first, and if you aren’t familiar with it, I’d recommend consulting with a local Realtor or attorney to help you protest your taxes.