If I already filed my taxes with turbo tax but the IRS hasn't accepted them yet could I go file my taxes with like Jackson Hewitt without any problems?

The IRS is not accepting any 2019 tax return until January 27.  Except for a few test batches.

See this IRS website - https://www.irs.gov/newsroom/irs-opens-2020-filing-season-for-individual-filers-on-jan-27

If you already submitted to Turbo Tax you have to wait and see if the IRS accepts it when they open.  If they reject it you can leave and go somewhere else.  You are stuck waiting.