I am a low income person and I am going to get an inheritance of about $25,000. The mony is from a distance cousin once removed. Do I have to
Include that amount on my income tax return. :(

No, but with a caveat: you do not owe any taxes on this to the US government - as the US does not have an inheritance tax - but a few states do have an inheritance tax. The US government and many states have estate taxes, but it applies only to very large estates and the executor of the estate would be responsible for paying any estate taxes out of the estate's assets. The heirs are not responsible for paying estate taxes. However, some states do have inheritance taxes - you can check out your state at the following web site:

Taxes by State