It's scary when someone says "3rd degree burn". Even if that's not what it is, it still implies a fairly significant event which should have been urgently examined and treated.
Concern for sealing a wound implies broken skin; at least a blistering 2nd degree burn. Probably the only fair thing to say is wait until there aren't any more blisters or scabs, the itching abates, and the raw skin no longer has a moist appearence; certainly no oozing/weeping. For small burns, that might take a week or two at the very least.
Something like petro-jelly certainly isn't the first thing to slap on a burn. But after the burning process has been stopped and any dead skin cleaned away, such goop helps preserve moisture and cleanliness; mild topical antibiotic creams may be used but aren't substitutes for basic cleanliness. Semi-permeable barrier films like Bioclusive(tm) and Tegaderm(tm) are waterproof but AFAIK not proven in deeper than surface conditions. Durability under active conditions is also questionable. Using these usually requires some instruction.
Even a small 3rd degree burn -- say, about 1cm in diameter -- is still serious stuff and should be professionally managed. Dead tissue is toxic, nothing good can grow from it and is removed to the extent possible. Regrowth progresses slowly inward from clean margins and usually requires careful management to reduce scarring and loss of function.* Consequently, even a small burn can take several weeks to heal properly. People working with welding equipment, molten material, or exposed to electrical arcing are at particular risk for such intense spot burns. Otherwise, such burns tend to be extensive because of inability to escape; either entrapment, physical disability, or altered mentation including drunkeness and unconsciousness.
*Here's when plastics really prove their worth.