Do I have the right to a court appointed attorney if I can not afford an attorney and I am not facing jail time even though I am facing suspension of licence and points against them.
In the United States, the case of Gideon vs Wainright (1963) held that a person charged with a crime punishable by imprisonment must be provided with a lawyer without charge if s/he should not afford one, .(See the Wikipedia article on the case.)
In Gideon this right was granted to anyone accused of a felony punishable by 5 months or more in jail. in Argersinger vs Hamlin (1972) and Scott vs Illinois (1979) this was extended to cover any criminal charge punishable by even 1 day in jail. In Alabama vs Shelton (2002) this was extended to apply to a conviction that resulted in only a suspended sentence of 30 days, with no actual jail time imposed.
According to the Wikipedia article on US Public Defenders:
In US civil cases (e.g., personal injury or a landlord-tenant dispute), public defenders may be appointed in civil cases that are quasi-criminal in nature (e.g., removal of children from parents and civil commitments for alleged sexually violent predators) or in highly unusual situations where the civil proceedings may be highly connected to criminal proceedings; otherwise indigent litigants are referred to a legal aid office. )
In many US states legal aid may be available for people faced with an encounter with the court system who cannot afford a lawyer. The exact standards, both for what kinds of cases are covered by legal aid, and what the financial limits on applicants for aid are, vary significantly between states.
This answer is entirely on US law. Other answers may cover the laws of other jurisdictions.