I'm sorry you feel so bad, J..
Our parents are also far away and when my son was born, nearly 3 years ago, we were still both grad students.
We just arrived in the United States and knew nobody who could help us.
And, another thing that made it worse to accept was that all our friends were also students - child-free students. So, all what we would hear all day was about this or that party/restaurant/concert... and we strongly felt that we were missing on something. I confess that I often would envy them, especially on Saturday nights ;-)
It was easier for us than for you to cope because we were older and already had enjoyed the student's night life enough in our past.
Now, we are not students anymore and most our friends are parents. So, they all face the same struggle of "how to have a date together without the children".
It's always easier to accept our difficulties when people around us face the same. Most of my friends now share the same concerns as I do (picky eaters, sleeping through the night, finding me-time, dating husband...), so we can vent together and feel part of the mom community.
But, being the one who cannot go out because of the baby, when it seems that everyone else is having fun and spending their Saturday partying is hard. Just remember you're not alone struggling with finding time/money/help to go out. Many - if not most - moms of babies on this forum face the same issues.
You may try to find a baby sitter, not several times a week, but once a month and have her come after baby is asleep. Her only responsibility would b quiet, so baby remains asleep and you wouldn't need to stress so much about finding a person you know and trust, as you do with your grandparents.
As you wrote, you have a wonderful life, and this is just a "detail" you wanted to vent on. In a couple of years, you will have a degree, a job and some more money to go out and enjoy. You have a great baby, husband, house, dog... You are blessed. You are preparing yourself for a great life. Don't let anger or envy mask all your blessings or ruin your happiness.