Therapists have an ethical duty, not just to their individual clients, but to society at large to promote mental health. Most therapists devote a portion of their practice to low-barrier services for those who can’t afford therapy or who are not insured. Be up front about your situation. Most therapists are deeply empathetic and genuinely want to see you get the help that you need. If the low-cost portion of their practice is already full they can likely refer you to low-barrier services.
Low-cost services are available with intern counsellors at excellent services such as Moving Forward Family Services