No you're not doing code reviews properly (obviously!). So the question remains whether there's something wrong with your code that it needs review sessions? (ie if you're shipping working code, code reviews are a solution looking for a problem).
If you think they would be beneficial, then I'd start work with a code review tool you can use in a 'as and when' mode - so you upload a code review request but it doesn't stop the rest of the process of committing and building code from happening. I think if you added the review to the workflow process that prevented commits until after review, you'd just end up frustrated and sidestepping the reviews. Be honest with yourselves in this case.
But if you could review code when you have time, then it becomes a good way of showing what you did to solve a work task, and you can always retroactively fix code review defects by raising a subsequent bug.
Good code review tools are ReviewBoard - a python base website. You upload diffs to the site and can then assign and comment on them. VMWare developed it for their own purposes.
Gerrit works well if you use git.
Redmine has a nice code review plugin that allows reviews based on any commit, you just create a new review as just another tracker ticket. Its pleasant to use and doesn;'t get in your way.