Should i use additional birth control when using the rhythm method, or is it fool proof?

Yes: Yes, you should use additional birth control, especially around ovulation, the week before and for a few days afterwards. Even when done perfectly the rhythm method has a 20% failure rate as ovulation can occasionally occur earlier or later than expected.

Not fool proof: Although the rhythm method has been used for generations it is far from fool proof. It may reduce the risk of pregnancy some, but over time it is likely to fail.