I moved from one state, my original and current workplace, to another and now work in both places.
As self-employed, yes. While the Tax Cuts and Jobs Act has eliminated (or suspended) these deductions for employees, self-employed individuals are still allowed to claim these deductions on their Schedule C. Here is an FAQ that reviews these and other expenses. https://ttlc.intuit.com/replies/5559255
I'm confused because on the IRS site it says you cannot deduct travel if the job lasts more than 1 year.
That applies to employees, which are not allowed the deduction anymore regardless. You are a business owner. Your travel in between your business locations for management duties is an "ordinary and necessary" expense for the operation of your businesses that is very much deductible. You need good records of the travel, but the expense is deductible. Of course, you also have taxable income in two states as well, so you also have two separate state returns.
One more question, in past years I only worked in Fl, where I originally lived, and traveled from my new home in TN. Would travel still be deductible in those years?
Probably not, because without your business in Tennessee, your tax home would have been Florida, making the travel to and from Tennessee a personal expense and not a business necessary expense.