I have been in similiar situations really often during my Bachelors (always fighting with different software plaftorms for sharing code - at the beginning of Bachelors, though - as we were not so advanced).
I was (like every other student) then introduced with the GIT and this is the thing that I would highly recommend!
If you, however, happen to have some merging problems, then just try using one of the following commands:
git fetch origin
git reset --hard origin/master
Good luck!
I'm not sure if it works the same way in SourceTree but in Git, you can create a merge request when you commit new content, and assign someone to resolve any conflicts. It might also be better if the same person is responsible to deal with merge requests (since it is a small project) to avoid confusion and unauthorized merges.
You can also remove files from the repository based on your .gitignore without deleting them from the local file system :
git rm --cached `git ls-files -i -X .gitignore`
Or, alternatively, on Windows Powershell:
git rm --cached $(git ls-files -i -X .gitignore)
Usually many code editors today are using a git plugin that you can use. Try to find if there is an intergrated Git versioning system in your code editor. Personally would reccoment for Mac using the Visual Studio Code which has git integrated