Gas Gauge

My gas gauge recently has gone on the fritz. Never had issues with it, but being gas is so much money I only put like 20 bucks in at a time. I finally had a chance to completely fill it and not it will show full for about 30 seconds then drop to empty and the empty light comes on also that happens the whole time bouncing back and forth drives me nuts I cant afford to always fill it, I know about how many mpg I get so I should be ok there, its just I want to know if its an eeasy fix. Also wondering if the fuel pump could be the problem. I know what the fuel pump is but just wondering if there is a sensor on it that could be bad or if the gas tank sensor thing is a different part. Any ideas would be greatly appreciated! Also if you know whats wrong if you can tell me what the part is called that would be helpful lol