Just to put it out there, under the modern understanding, world-wide, and even from the perspective of the law in India, trans* and transgender includes everyone whose gender identity does not match what they were assigned at birth, and this gender identity can be anywhere in the vast spectrum, and includes what you're describing here as "cross-dresser"
Another thing to note is that the term "cross-dresser" is generally deprecated because of the implication that the person is not "dressing for their gender" or is somehow living a lie/tricking others, and reinforces outdated gender stereotypes and norms that do more harm than good.
Instead, there are multiple nuanced non-binary identities like bi-gender, genderfluid, genderqueer, etc that may instead be used as appropriate. Of course the trans* umbrella term/identity is also available for use.
You also have the option of being cis and gender non conforming/gnc as well, and wear anything you want, etc, again fully based on how you see yourself and how you perceive your lived reality.
Kindly read through https://genderdysphoria.fyi/ which is an excellent guide on the variety of ways Gender Dysphoria manifests, and the broad set of ways some one can be trans* or transgender
