I can empathise, as you will see in my answer to How strict should we be with Not An Answer flags/closure on new users?
I would encourage both you and your cousin to include contact details in your user profiles like I have done in mine. You can tailor your profile to each site that you participate in.
I think it is OK to use comments to direct each other to look in your profile for contact details, because comments are considered temporary and can be deleted at any time, but I do not think that such comments should ever appear in either a question or an answer which are intended to remain on the site in perpetuity.
I think this reflects the Stack Exchange network-wide policy at Any way to send a personal message to another user?. However, even using comments in this way may be problematic.
