Yes, you can file RTI Application to a High Court to know about the Status of your Case.
High Courts are Bodies carrying out functions of the Judiciary and are "Public Authorities" as per Section 2 (h) of the RTI Act 2005. You can address the RTI Application to the designated "Public Information Officer (PIO)" appointed by respective High Court. The mode of fee payment and the prescribed fee varies for few High Courts.
To know more about the procedure to file RTI Application, please refer https://onlinerti.com/