You should add the other session if money is not an issue.

You're putting yourself in an impossible situation, you are trying to push yourself to be OK but you also know you're not ok. You know what you NEED to be okay (more time to talk with your therapist and sort out the multitude of feelings).

No need to be so hard on yourself. You have a therapist for a reason, they're part of your support system. And if they're the support you need right now that's fine!

Learning to accept help is probably more of a goal for you than remaining independent. At least, that's what I recognize from your last paragraph. I know this feeling well - not wanting to risk becoming dependent. But one extra session won't suddenly throw you into dependence, really.