I don't like using a transliteration if I haven't seen it being used elsewhere first, but I just can't find some of the spellings I want to use. My concern is this: If e.g. "yhhuh" isn't an accurate rendering of בֵית, who's to say that "bhait" is? What should I do? Sorry if this is off-topic, but I don't know where else to put it.
Fundamentally, the goal of any language use is to communicate to someone. Anything that helps this communication is useful, and anything that gets in the way of communication is not.
So which transliteration to use comes down to who you want to communicate to, and why. If I want to transcribe an Egyptian word:
The first step is to ask why I'm transliterating it. Am I writing to Egyptologists? I should use an Egyptological transcription like 3st. Am I speaking out loud to Egyptologists? I would pronounce it aset. Am I trying to add some foreign flair to a historical novel? I could transcribe the pronunciation into something like rhuusat. Do I want to talk about a particular Egyptian deity to an English-speaking audience? I should use the Greek-derived transcription Isis. Do I want to talk to someone about these particular hieroglyphs? I should use their Gardiner numbers,
Q1 X1 B1.
None of these transcriptions is wrong. Even rhuusat, which is something I came up with ad-hoc to represent Old Egyptian
/ʀuːsat/, works perfectly well for its purpose (representing the original pronunciation well enough to add flavor to a piece of fiction).
So, you need to ask yourself—what's the end goal of this transliteration? There are quite a few different standards out there, for all sorts of different purposes, and you can probably find one that fits your needs. And if none does, there's nothing wrong with tweaking them or coming up with your own.
It sounds like you have a particular transliteration in mind already ("I just can't find some of the spellings I want to use"), and want permission to use it. In which case, go ahead. Really. There's no transliteration police that's going to break down your door and arrest you for using "y" instead of "i" for yodh. Just ask yourself if it effectively conveys the information you want to convey, to your intended audience.
"The Authorities" are to say, and there can be competing authorities. For probably all languages not written in Latin script, there is some standard convention for transliteration. Many times, there are multiple conventions. There are a few different ways to transliterate Russian, and you can read up on the various systems on that page. With Hebrew, you have the "which language" problem so that the conventions for Biblical Hebrew are not the same as the conventions for Modern Hebrew. Transliteration schemes often derive from scholarly convention, but there are also governmentally-established norms which compete, such as BGN/PCGN, which offers this for (Modern) Hebrew. It's similar to the question, who's to say that "cat" is spelled "cat" in English? There is no such thing as the dictionary, but we all agree that it's spelled "cat" unless a quirky individual wants to spell it "kat". Conventions can be flouted, and a systematically-flouted convention can become a competing convention, if enough people decide to follow suit.