First of all, you are to be commended for recognizing that you have a problem and assertively taking a
step toward correcting it.
This type of question should be discussed with a trusted Rebbe or Rav who knows you
personally, understands your situation, and can therefore offer guidance that is tailored specially for you.
He may suggest that in such cases you can drastically shorten your davening, which would make it less daunting
and more easily doable in your circumstances, and he will specify how much you should shorten it based on both
your conversation with him and his knowledge of halacha.
It's also important to note that given how difficult it is for you to daven, it is so much more
meaningful and precious to God when despite it all you put in that extra effort and force yourself to do
it only because He wants you to and not out of habit and convenience. I personally envy the power of such a prayer.
As far as making it up to God - it's like anything else: you do teshuva to the best of your ability, which you
have already begun by taking this step. Keep in mind that teshuva is not all-or-nothing; each part of the teshuva process
counts for something by itself, even if you can't complete all the steps (Mabit in Bais Elokim). Every little bit you do to turn toward God is meaningful and significant.
[not] allowed to do "tashlumin" for intentionally missing a prayer.
True. But depending on what the OP means byno desire to Daven
, the psychological factors that are keeping him from praying may make this a case of ones or tarud rather than a violation. See Rambam (Hil. T'filla 3:8, "בשוגג או שהיה אנוס או טרוד משלם אותה תפלה בזמן תפלה הסמוכה לה", in light of 4:15 "כוונת הלב כיצד כל תפלה שאינה בכוונה אינה תפלה... מצא דעתו משובשת ולבו טרוד אסור לו להתפלל עד שתתיישב דעתו"). – Fred Aug 18 '16 at 18:07