This documentation from JIRA provides you simple steps on how to add a custom field on JIRA for your own project, but for this to happen - you have to be a JIRA Administrator. This can't be helped much, as this is a limitation from JIRA itself.
But having said that, if you get it sorted from a JIRA Administrator from your Organization - getting the details of the newly added custom field is not that difficult. JIRA REST APIs will come to rescue in that scenario.
You can simply fire the following REST GET API call to get the details that are intended to known by you!
curl -D- -u fred:fred -X GET -H "Content-Type: application/json" https://jira.fred.com/rest/api/2/issue/FRD-88651
The call will further provide you the necessary details! Hope this answers your query!