t-SNE for 2d points? I want to visualize 2d embeddings of my deep learning model. Since my points are already 2d, can I directly plot them and see if there's any clustering or do I need to use something like t-SNE?

The point of t-SNE is to reduce the dimension to something that can be visualized in two dimensions (maybe one or three), without sacrificing too much structure. Your data are in two dimensions, so the best way to reduce to two dimensions without sacrificing structure is to do nothing; just graph your scatterplot.
EDIT
To answer what I posted in a comment to the OP, the t-SNE indeed does something. (I divide by $10$ at the end to help the visualization, but that only affects the zoom, not the shape.)
library(Rtsne)
library(ggplot2)
set.seed(2021)
N <- 1000
x <- rnorm(N)
y <- rnorm(N)
tsne <- Rtsne::Rtsne(cbind(x, y))
d0 <- data.frame(x = x, y = y, Group = "Original")
d1 <- data.frame(x = tsne$Y[, 1]/10, y = tsne$Y[, 2]/10, Group = "t-SNE")
d <- rbind(d0, d1)
# plot(tsne$Y)
ggplot(d, aes(x = x, y = y, col = Group)) +
geom_point() +
theme_bw()


