2009 Chevy cobalt cranks but won’t start. Advice and suggestions?

My 2009 Chevy cobalt has been running just fine except for a surge in the car from time to time (feels like gas peddle has been used and rpm fluctuations at a constant speed). However, I got out of my car and turned it off for 3-5 minutes and went out to start it but it wouldn’t start but it cranks. Tried jumping... show more My 2009 Chevy cobalt has been running just fine except for a surge in the car from time to time (feels like gas peddle has been used and rpm fluctuations at a constant speed). However, I got out of my car and turned it off for 3-5 minutes and went out to start it but it wouldn’t start but it cranks. Tried jumping it for the hell of it and nothing. Went back to try again later that night before it got towed and it started up just fine. Drove the car home and then started it off and on a few times, all starting perfectly. Weird, but thought we were okay. This morning I went to start the car and it started and then died immediately after and has t started since. The car cranks still. I check the relay and the relay isn’t the issue. Does it need a fuel pump replacement? The fact that it started and ran after Initially dying is confusing me. Thoughts, suggestions?
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