My file was delivered early March, but I got no refund. I got one stimulus check based on my Turbotax info, so I assume they started processing but should I be worried?

 This year is taking the IRS longer to send the refunds. There are millions more people filing returns to get the Stimulus payment.

See this news article on Refunds being delayed
https://www.msn.com/en-us/money/personalfinance/where-is-my-damn-irs-tax-refund-new-answers-emerge-a...

Only the IRS can tell you. If your return was Accepted then check IRS Where's my refund
https://www.irs.gov/refunds/

When will you get your refund?
https://ttlc.intuit.com/community/refund-status/help/when-will-i-get-my-irs-tax-refund/01/25589

IRS - Questions about Refunds
https://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions

From this IRS website - https://www.irs.gov/newsroom/irs-operations-during-covid-19-mission-critical-functions-continue

As of May 15, 2021, we had 300,000 individual tax returns received prior to 2021 in the processing pipeline. Including current year returns, as of May 15, 2021, we had 16.4 million unprocessed individual returns in the pipeline. Unprocessed returns include those requiring correction to the Recovery Rebate Credit amount or validation of 2019 income used to figure the Earned Income Tax Credit (EITC) and Additional Child Tax Credit (ACTC). This work does not require us to correspond with taxpayers but does require special handling by an IRS employee so, in these instances, it is taking the IRS more than 21 days to issue any related refund. If, as a result, a correction is made to any RRC, EITC or ACTC claimed on the return, the IRS will send taxpayers an explanation. Taxpayers are encouraged to continue to check Where’s My Refund? for their personalized refund status and can review Tax Season Refund Frequently Asked Questions.