You will need to review your plan by going to the IRS website for payment plans here. Scroll down to the section titled "How do I review or revise an existing plan."
You will be prompted to log in and should be able to view any payments made to your account.
You can also sign into your Online account with the IRS to view your payments and the balance due.
As far as how long does it take for the IRS to reflect the payments, you would also need to directly reach out to them. You can check your bank statement as well if you chose to make payments directly from your bank account.