Hope you are doing great!
Could you please confirm that the setting mentioned below are enabled at your end?
Dashboard >> rtMedia >> Settings >> BuddyPress >> Allow upload from activity stream
If you are not able to upload media from media tab, please also turn on this setting :
Enable media in profile
Dashboard >> rtMedia >> Settings >> BuddyPress >> Enable media in profile
You can visit this documentation for more details on rtMedia admin settings :
As per the requirements you have posted, these two options are a must. If any of these is disabled, the feature will not work the way you wish.
Kindly let us know if the issue still persists.