The thai banks don't open accounts for visitors I.e. tourist visa 's or visa exempt etc. As you are not going to be a permanent resident. The long term visa's demonstrate you have intentions to stay i.e the O visa ( in country or from your own country through the thai embassy). So to get a bank account without using a workaround ( an agent) its best to come with an O visa or an O-A visa ( or others) from your own country ready prepared. The reason why you need money in a thai bank account is to show you have funds in a local account should you need it in an emergency ( no health insurance requirements with an O extension in country)
remember aa DTV cannot be applied for inside of thailand you have to apply at an embassy other than thailand, your home country or country near by. Agents can only help you prepare for a visa as its not within thailand they are granted.
if it's s tourist visa it only gets you 60 day stamp for entry into thailand. You have 90 days to use the stamp suggest you read again what you have been given. You can get a 30 day extension inside of thailand at a local immigration office once you arrive if you want 90 days
I doubt you would have been granted a 3 month visa unless you applied on a retirement O or other long term visa. The visa i believe you have is a 60 day tourist visa which you have 90 days in which to use it. Not a 3 month visa. You will get stamped in for 60 days the same as visa exempt