If you feel you need the therapy, then you have the need. Yes, there may be people worse off than you, but there are likely people better off than you (mentally) who use the clinic. I would just go have a consultation with them, ask about the type of therapy they use, etc. Even if the focus is CBT, you might be able to find a T there who does not strictly adhere to that format (my T is trained in CBT as well as other methodologies). I think it's at least worth giving a shot...

I'd also suggest talking to a therapist (whether there or your regular one) about how you feel like you shouldn't get therapy because there are others more deserving. Sounds like it could be something from childhood maybe... Out of curiosity, do you generally feel like others should take priority over you in other areas of life? Or that you're not deserving of what you have?