i have 13 days vacations and I just gave my 2 wks notice..do they have to pay me? company does not have employee handbook

Under the Texas Payday Act, which governs payments of wages to employees, an employer is not required to pay accrued and unused vacation, sick leave or PTO to departing employees unless it has a written policy stating that it will do so.  Your question states that the employer has no employee handbook, which is where such policies are typically found.  Unless there is some other written memo, policy or promise to pay such amounts, the employer is not required to do so.