I don't have a spleen, what are my chances for getting systemic sepsis?

Higher but still low. There is no published data on rates of sepsis or septic shock in patients with splenectomies (or who are congenitally apslenic, or functionally asplenic from other causes); your risk is higher due to susceptibility to encapsulated organisms. Hopefully, if it was a planned splenectomy you had a pneumonia vaccine prior to your surgery. The vaccine is less useful (or even useless) afterwards.
See below. In children an incidence of post splenectomy sepsis(pss) is one per 175 patient-years. Pss frequency is more variable in adults one case per 400 to 500 patient-years. To lower your risk you should have received pneumococcal vaccine, conjugated hemophilus influenza polysaccharide vaccine and quadrivalent polysaccharide Meningococcal vaccine. You should receive an influenza vaccine each year.