Can cancerous tumors in the groin shrink on their own and then swell back up?

Groin nodes. Are found in few cancers and lymphoma. Cancers do not wax and wane, but lymphomas might.
Yes. Some types of low grade tumors can shrink & grow. "growth" may mean sudden bleed in to tumor then it would feel swollen & possibly tender. If biopsied, there may be infection causing "growth".