Can nomination be part of the workflow for CiviCase?
I'm not sure you need CiviCase but it sounds like it could fit. You might also want to take a look at CiviGrant. For the form you might want to also look at https://civicrm.org/extensions/webform-civicrm-integration, especially if you're using cases since then it can generate a case from the form.

If not using cases, regular activities have both a submitter and "with contact" field to track submitter and recipient, or if you want to keep those fields for other purposes they can have custom contact reference fields.

The answer might also depend on what kind of reporting you need. For example cases might make it easier to count groups of related activities as one, e.g. if the same person gets nominated for funds again the next year.