I accidentally made a commit in the wrong branch but since I can do Amend I'm thinking if it's possible to use it to transfer the changes to the right branch. Can I change branch instead and do the amend there or will it be applied to the same branch where it was committed?
Assuming you have not yet pushed the first branch with the mistaken commit, you may try cherry picking it to the right branch, then rolling back the first branch:
# switch to correct branch, and cherry-pick desired commit
git checkout branch2
git cherry-pick <SHA-1 of commit>
# then switch to first branch, and remove incorrect commit
git checkout branch1
git reset --hard HEAD~1
The <SHA-1> of the commit you want can be found by using git log branch1. Note that if you have already pushed branch1, then a safer option would be to git revert that commit. But, you may still use cherry picking to move the commit to the second branch.