Did snap make an unbreakable vow with bellatrix?

No, Severus Snape did not make an unbreakable vow with Bellatrix Lestrange. Instead, he made an unbreakable vow with Narcissa Malfoy, Bellatrix's sister. This vow was to protect Draco Malfoy and, if necessary, to kill Albus Dumbledore. The intricacies of this vow and Snape's motivations are explored in the "Harry Potter" series.