If by "follow the Old Testament" you mean "Must we keep the Law of Moses?" the answer is no. However, we cannot understand the New Testament without having at least a broad understanding of the Old Testament. For example, consider the very first verse of the New Testament:
Matthew 1:1 The book of the generation of Jesus Christ, the son of David, the son of Abraham.
If you are not familiar with the Old Testament, you will know nothing about David or Abraham or the promises made to them and why they are so important to God's work of salvation that they appear in the very first verse of the New Testament.
Here is a link to information on the website which you will find helpful (please click on the title):
I hope you have found this helpful.