I had the same problem 2 weeks ago with my 1991 acura integra gs. I have an automatic so for me it was the transmission. If this sounds familiar that's what it is. Basically I would start the car fine put it in drive then after about 10 feet it would make a clicking noise. After driving for a bit it would stop. But once off and turned on again same thing another 10 feet clicking starts the. Goes away and it comes from the front so may sound like engine but most likely transmission also mine shift hard when putting in drive reverse and park. If automatic depending where you live or mechanic I have a good mechanic that is going to fix mine by replacing it with a used one for 800 another mechanic can also rebuilt it for 1200 right now I'm debating what I should do.

No but I commute 70 miles a day

if it's a stick you need a clutch...if it's an auto, you need a new tranny..

The teeth on your clutch may be bent

do you race?