Make My Trip - Extra charge incurred on my trip due to MMT agents mistake

I had booked a package from Mumbai to Shimla/Manali and Chandigarh then back to Mumbai. My booking Id was NL*************. I was travelling with * adults and a child and in all, we were *. The agent sent me a form to be filled up and all details were filled and sent to the MMT. We received the vouchers which defined the exact date of births of all individuals travelling on that date. My child turned * on the *st of June ****. Our travelling date was **th June ****. The package booking was done in mid of May ****. Unfortunately, the agent did not book the tickets for the child thinking her as an infant. My child flew from Mumbai to Chandigarh without a proper ticket which is quite a loss to the airlines and a wrong part played on my understanding too. Unfortunately while returning from Chandigarh to Mumbai the alert staff of go air pointed out that the child is not an infant and she will require a ticket to travel. Firstly I was removed from the queue and was asked to wait on the side. Secondly, my child had to be kept waiting for almost an hours time to get things sorted. Thirdly an embarrassment was faced heavily since I never faced these issues when I booked things on my own. Now when I asked the department why this had happened they are putting things on me stating that the age was wrongly entered by me and a screenshot of the same was shared by them to me on my mail. This mail was a big fraud as I have the vouchers which mention my children date of birth proving that I had correctly entered the details and the mistake was from their end and not mine. I was also waiting to solve this issue by getting a call from them however when they actually called they started speaking in a bad tone to suppress my claims and voice so that I don't go the distance with this.