The size of your antenna has absolutely NOTHING to do with your supply voltage.
If the calculation you have made for your antenna, per your transmitter frequency, is 80 cm, that is exactly how long the antenna should be. The 20-30 cm antenna you have fabricated is presenting an improper impedance to the transmitter power amplifier and will cause it to get hot and burn up. Not only that, but it will simply not work efficiently and much of your transmitter power is wasted as heat in the antenna itself.
If size is a concern, there are loaded antenna designs that allow shorter elements... They are not as efficient as a properly tuned antenna (there will be loss), but they do at least keep your amplifier from getting too hot because the impedance the amplifier sees is a match.
Here is an absolutely thorough discussion of antenna loading:
Mobile antennas, short verticals, loading coil loss,and loading coil current
But keep in mind, your OPTIMAL antenna length depends on frequency. Voltage is not a factor in determining antenna length. If your calculation says you need an antenna X long, either build an antenna that is X long or devise a loading coil to cancel capacitive reactance which allows a physically shorter design.
Oh....one more thing. It is extremely advisable that you either build or purchase an antenna analyzer and perhaps a field strength meter for your experiments. Without test equipment you are running blind and the only practical test of your equipment efficiency would be to measure the temperature of your amplifier while transmitting and perform receiver tests from a distance. But even then you would be working blind.
At a MIMIMUM I might advise an VSWR meter to monitor standing waves on the system, which can be of assistance in tuning your antenna if you use it properly.