Rate hikes might be a small factor but they don't affect the debt service on the debt issued prior to the rate hike.
Of course, the new debt, including the rollover of the prior debts, will be at the higher rate but I think the Fed's action was too recent to have a big impact on these numbers.
There are many articles on the subject. Do a search using these terms “fomc rate hikes budget deficit”. Don’t use the quotes.
Obama and company timed a lot of stuff for after he left office. I believe the rollover of much of his debt hit after the hike.
When Obama ended his terms, the interest rate was increasing from .5 to .75%. It is now at 2.5%. While it is only a portion of the debt, it is an increase to 500% of what it was.
https://fred.stlouisfed.org/series/fedfunds
Didn't Obama shift heavily to shorter-term bonds as well? That'll make the rebound effect even faster.
Debt service was up 90 Billion in 2018 as compared to 2016 - or roughly 17.5%, on increase in debt of about 7%.
https://www.treasurydirect.gov/govt/reports/ir/ir_expense.htm