Broken links when packaging in indesign

I am currently a student in Graphic design and we are working on a project where I have to package my files and send them to other classmates. I usually don't have any problems with this but the past two projects have been having broken links in the indesign file. I seriously don't know what is happening. When I package the file and open the indesign file from the packaged folder all the links look fine and are linked to the packaged folder links folder. When I send the packaged folder out, classmates are telling me that the links are broken but they are all in the links folder. I have not been able to figure out what is causing the issue. Something I noticed is that when I download the packaged file, the links are getting pulled from my computer instead of the downloaded packaged links folder. I have tried re-linking and packaging multiple times but it keeps happening. I don't know what to do. I would greatly appreciate it if anyone could help out with this, I don't imagine I would be able to hold a job long if my laptop keeps sending out broken files. Thank you.