Will your stipend be reported on a 1099Misc? If so you will receive that form by the end of January. You say they suggested that you pay estimated tax ahead of time, but now it is 2020 and it sounds like you did not do so. If you want to make an estimated payment this late you can do it on the IRS site, or just pay the tax you owe when you file your 2019 tax return.
https://www.irs.gov/payments/direct-pay
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