Fully understanding the theory about why it's necessary to accept feelings, as explained in the EC book, can be helpful. Acceptance is a higher state of consciousness, closely aligned with witnessing, for which we slowly build our capacity. It takes time, a dedicated practice, and it's normal to fall out of the higher states.
Anxiety has both mental and emotional components. When the mind is resisting, anxiety is higher, as you describe. When the mind comes to rest, through acceptance and witnessing, anxiety is lessened. At this point, it is easier to see the core feeling behind the anxiety, which is likely to be fear-related.
The optimal strategy when anxiety comes up is to relax the mind, and go to the core feeling behind it, applying the ECP steps to that. You can also process the anxiety itself, if you can't immediately find the core feeling. If there are past incidents that come up related to the core feeling, that's helpful too. Let those memories trigger core feelings.
With acceptance, remember it's always the feelings you are focusing on and accepting, not primarily the associated events or circumstances.
