I'm 13.Can going to a psychiatrist affect my further schooling?

The only way that it will affect you is that you will be able to recover from your depression and have the ability to lead a happy and productive life. College and employers are not interested and don't ask if you have or are now seeing a psychiatrist. There are laws that protect you called HIPPA laws. That means that nobody can get your medical information without your signed permission. And if you don't want anybody to know you don't have to tell anybody. I just noticed that you said your mum so you are from Great Britain. The same rules apply but the HIPPA law is in the US. You should be proud of yourself for getting the help that you need. You sound like a very smart kid!