Negligence of duty causing undue delay

Hello Sir/Mam , I applied for a verification process online in a TN govt 'office X' on Nov 7 . Paid 10k for the application. They had to contact Embassy via email and complete the process ideally in 10 days . They didn't respond to phone calls . After waiting for more than a month , I went in person to Chennai and asked for an update on Dec 20 . They said they initiated the process long back and they were waiting for embassy's response . After another 15 days of waiting , I went back on Jan 5th , and got the same response , that they were still expecting embassy response . Tired of waiting , i contacted the embassy instead and embassy said , the process was initiated by office X on Dec 21 and concerned reply was sent to the TN office on dec 22 itself . It turns out that office X had been sitting on it for around a month and a half without initiating the process until I went in person and enquired . I also came to know that they have been doing this for many others as well . The TN office X's negligence has cost me almost 2 months of my career . Is there any possibility to sue them for the delay and the depression it caused ?