Engine Grumbling. 2007 Honda Civic.

kelemenopy

About a week ago, I accidentally let the oil in my 2007 Civic get very low, right before getting the oil changed. It had been almost 7,000mi since the last oil change, and the car has 79,000mi on it. The day before I changed the oil, the engine started grumbling and shuddering. Since changing the oil, this same thing happens (same low rumble, with some shuddering) for the first 5 or 10 minutes after I start up the car in the morning. After that, it noise tends to disappear, and the car runs normally for the rest of the day, as long as the engine is hot.

• Any ideas about what the issue could be? I've stopped by a few shops and got a lot of different answers. One mechanic told me the engine needs to be replaced, and another one told me that I'd be safe to take the car on a road trip. Another told me to replace the spark plugs.
• It's worth noting that no lights have come on in the dash.
• I know nothing about cars. Can anyone help me figure out what to do?