Yes, if she inserts the bedikah cloth into the vaginal canal as deeply as she can and rotates it in the folds as well as she can, that is acceptable for the hefsek taharah. Although it is important to do your best with every bedikah, it is especially important to be as thorough as possible with the hefsek taharah and the bedikah on day one of the seven clean days.

Since your vaginal canal is dry, you may find it helpful to moisten your bedikah cloths slightly prior to use. Alternatively, you could try out one of the vaginal lubricants on the market. They often claim that the moisture lasts for many hours after application. You would not apply immediately before the bedikah, but the product could help. If your dryness persists, you may wish to consult your physician, since this can have implications for bedikot and for relations.