Airtel - Airtel postpaid bill dispute

I have Airtel Mobile postpaid plan of ***. In the month of July ** went on an international trip to the USA. After coming back to my surprise my bill for the month of July came as *****+ Rs. My bill shows I have sent ** SMS to a particular number. But when I check my phone message log there is no record of outgoing messages. Also, personally I have not sent any messages.
Also, my bill shows that I have used mobile data worth of ******/- INR which is ridiculous. I had disabled my data on airtel sim and I was using US local sim of Lycamobile. Another point to note is the time of usage mentioned in the bill indicates for most of the entries of either morning or evening IST time. Since the place, I went to is **:** hr behind during that time I should be inside my hotel where I was using hotel Wifi. The bill does not make any sense. Another point to note is I have never requested to enable any international roaming services from Airtel. I am a frequent traveller and this is the *st time it has happened.
I have called airtel customer care regarding this. But they say that they enable international roaming services automatically and data bill has come *.*l But I have to pay only **k and bill is valid and there is nothing they can do.
I am not sure how the bill is valid.
*. I have no record of any messages sent from my mobile but the bill shows that messages are sent.
*. My data and Volte on Airtel sim was disabled. There is no way my mobile would be using Airtel data on roaming (I keep my data roaming on disabled mode always.)