I'm not saying this to be judgmental at all, because I felt exactly the same way myself, but is it possible that you feel so uncomfortable because you believe those mistaken thoughts? You're feelings aren't for no reason, you feel the way you feel, but there are other ways to think about the situation which may also begin to change the way you feel about it. I can only be so sure about that because I worked through it a fair bit myself. Like I worried that I'd be less important to my therapist or less deserving of her time (particularly outside of my appointments), but she hasn't treated me that way for a second, or changed her opinion of me at all, so although it was a valid concern and feeling, I no longer worry that I'm less important to her because of the money side of things, because she's shown me that it's not true.

This money stuff can also bring up other important stuff within therapy too. I realised how caught up on money I always was. I even realised that I felt I'd taken advantage of my mother as a young child any time she spent money on me, and so on. I was having such a big reaction because I felt I didn't deserve money from other people, and as a child I began to worry about money and needing to be the one in control of finances. So accepting what my therapist offered was very hard for me. I thought all of the same things you listed, as well as things like I didn't deserve to take it whether she offered or not.

Money is hard, your feelings aren't wrong, but I do think you need to talk with your therapist about this all again.