Yes let her know that you scheduled without considering your finances, and that as a result you feel you need to cancel.

Rather than asking her for an unpaid session, you could ask if she could defer your payment for the session. Or could she accept something like an extra amount in your regular payments ($5 or $10) until the session is paid for, then returning to the regular fee.

Definitely let her know what's going on and see if the two of you can work out a solution that meets both of your needs. Let her be part of the solution since it affects her too. In fact, I would imagine this won't be the first time she's been presented with a patient's financial issue, so she may have a plan for handling in place when it happens. So let her know, let her in on this and see what the two of you can come up with.

good luck to you!