Hi bro,
There are Hebrew resources on afii.org, and the Newberry Bible has good Hebrew notes, and an introductory section on the names of God. Here is an excerpt from his note on 'Jehovah'.
After mentioning the number of times it's used, and references for when it's not translated 'the Lord', he shows it in combination with Elohim (Jehovah Elohim) in Gen 1 and alone in Gen 4.
'The signification is - He that always was, that always is, and that ever is to come.' Then refs in Rev with detail about tenses. Note: in the English above, he has reversed the order the meanings are embedded in the name.
'First, YEHI, "He will be" long tense. Second, HOVE, "being", participle. Third, HAHYAH, "He was", short tense used in the past.' He then shows the Hebrew.
There is, online, the Sacred Names Bible, which is an easy place to search for all the times 'Jehovah' is used in the text.
The KJV has a system for translating Jehovah 'Lord', but there are other names of God which are also translated 'Lord'. I think you have a BIG study ahead!
Looking at Deuteronomy 6, Jehovah and Elohim are used together all through. I'm not quite sure what you're trying to disentangle, because 'Thy' is sometimes when God is speaking about Himself, or being quoted to the people, but not only.
And at Peniel, when one might have expected Jacob to use 'my' about God, he calls Him Elohim. Earlier in Gen 32 he prays: 9 And Jacob said, O ELOHIYM of my father Abraham, and ELOHIYM of my father Isaac, YHVH which saidst unto me, Return unto thy country, and to thy kindred, and I will deal well with thee:
You get the idea. May the Lord lead you and bless you as you study.