Students who want to take higher courses early
You may consider:


Transferring to another South African school that would be of a similar level but more flexible about the upper level classes.
See if you can find a way to go abroad.
Stay where you are but try to get into those higher level classes.

3a. Try to get permission directly from the instructor.  Maybe you won't get credit for the class -- but if you are permitted to sit it (audit) the class, that's progress.  A good way to start working on this would be to visit the instructor's office hours with a couple of good questions that will show your aptitude, level of knowledge, and communication skills.  After getting to know the instructor in this way, you could then ask for permission to attend his or her class.

3b. Try going above your department head.


I personally favor method 3b as the preferred approach -- if it works.

Now, what to do about your feeling of isolation?  Here are some ideas for you to consider:


Do some tutoring/mentoring/teaching.  This can be rewarding and can help you break your isolation.
Take some classes in fields where one might be able to apply some tools of applied math or statistics.
Get started with one or more interdisciplinary projects with folks in other departments.
Interact with mathematicians in other countries with email, letters, etc.  Here's one way to get started with this: read some papers you're interested in.  Write to an author of one of the papers, to say that you read the paper with interest; say what you found most interesting; ask something.  You could mention that you would be very glad to be able to correspond with grad students.  Then see if a correspondence relationship develops.