I need to create a text field option for miscellaneous issues that my agents can fill out in my drop-down list. Is it possible to add an option to enter a line of text?
No, it is not possible to add a free form text field option within a drop-down list.
A potential workaround is to include a field option for "other: see details," then add a separate corresponding "Details" field as a text field. This way your agents can fill out the field as needed.
For more information on custom ticket fields, see the article: About custom ticket fields.