Applying to graduate school or medical school is a complicated business. One important part of it is getting great letters of recommendation. It is too late this year to establish the relationships that form the basis of solid letters based on evidence, not opinion. But it is not too late to ask for the letters or to apply to graduate school.
One thing the programs all ask you when you give the names of your letter writers is whether you waive your right to see what those letters say. Nearly everyone automatically waives access. And so should you. There are strong reasons for waiving access. The first is that everyone does it, so you do not want to seem different in this way. It might imply you are a difficult person. No level of brilliance will get you into most programs if you are solidly perceived as a difficult person.
The second reason is that letter receivers want the letter to be completely honest and frank. The letters will be weighted less strongly if access is not waived. You probably have excellent letters, so you want them to count as much as possible. Anyway, to the extent US letters are ever negative it is by omission, not criticism. It takes a seasoned letter reader to even pick up these differences. So it won’t do you much good to see the letter. You won’t be able to tell a strong letter from a weak one.
If we had a system where all letters were open, it might be different. There are traps to not seeing the letters. I myself fell into them. One was that I later heard that someone had written me a bad letter for grad school. He said I was very strong willed and not afraid to voice my own opinions even when they differed from those of that particular professor. If you know me, you know exactly what to think of that letter, but in 1974, I’m guessing these were not considered desirable traits in female grad students, generally, though UT Austin delighted in them. That bad letter came from someone I had a couple classes from but did not know well, so remember to get to know 3 professors!
My second mistake was imagining someone wrote me a weak letter when in fact it was a letter stronger than I deserved. He ended up showing it to me to my great shame. So, I’m always happy to show people the letters I write for them. But come ask me directly. Waive your right to the letter.