You'll need to double check with the TD but you'll probably need to notate with your other hand.
Broken Arm Problems

If I remember correctly, the rules book says you can have a volunteer notate for you, but the same accommodation can be given to your opponent if he/she requests it.

If I remember correctly, the rules book says you can have a volunteer notate for you, but the same accommodation can be given to your opponent if he/she requests it.
35F10. Optional assistance.
A blind, visually impaired, or disabled player shall have the right to make use of an assistant, who shall have any or
all of the following duties:
a. to make the moves of the blind or disabled player on the board of the opponent;
b. to announce the moves of the non-disabled player;
c. to keep score for the blind or disabled player and to start the opponent’s clock;
d. to inform the blind or disabled player, on request, of the number of moves made and the time consumed by
either or both players;
e. to claim a win on time for the blind or disabled player or inform the blind or disabled player when the
opponent has touched a piece without moving it;
f. to carry out the necessary formalities in cases when the game is to be adjourned;
g. to pause the clock and summon a tournament director at the request of the blind or disabled player.
If the blind, visually impaired, or disabled player uses such assistance, the non-disabled player is entitled to and
must provide his or her own parallel assistance should he or she so desire.
TD TIP: Though not required to do so, the TD should do everything possible to help both the disabled and nondisabled players(opponents) to secure assistants. Often spectators or players with byes are willing to act as
assistants.
35F11. Assistance for the non-disabled player.
If the blind, visually impaired, or disabled player uses a special chessboard and does not require any assistance, the
non-disabled player may make use of an assistant, provided by the non-disabled player, who shall announce either
one or both players’ moves and make the blind or disabled player’s moves on the non-disabled player’s board. Note
that if acceptable to both players, they may both use the same assistant.
you were right

I once played an opponent that had a broken arm and the TD said he didn’t have to notate. But maybe because it was a 4th grade tournament.

You still have five weeks to get used to your cast and learn how to write left handed. It doesn't have to be neat because nobody will grade your penmanship.

When I broke my right hand, I sucked at writing with my left but I did sort of learn? Maybe you can still grip a pencil with your fingers. Of course it would be really hard. You can check with the TD and see if your allowed to have someone notate for you and then make plans accordingly.
So.. I am Planning to go to the US open, but I broke my right arm, and cant notate, do I have to write with my left, or do I not notate?