You need to exit and apply online for another Vietnam visa..
Not sure what passport you hold but you may be better off going to Cambodia as they have slightly more friendly visa options and visa on arrival for most passports.
Phnom Penh is nice city so I suggest you check that out..
DTV is Destination Thailand Visa and you may qualify depending if you are studying in one of the approved study areas that qualify for a DTV.
Other than that if you don't qualify then perhaps a 6 months multiple entry tourist visa would suit you which can be stretched out to 9 months depending on your exits and entries..
If you are planning on being in Thailand on a long term basis then either of those are safer options than trying to rely on Tourist exemption entries..
Both the DTV and 6 month multiple entry tourist visa need to be arranged outside of Thailand before you travel.