Q: Car doesn't have power in the lower gears.

I was driving my car and it worked ok in first gear, but it wouldn't gain speed in second gear. It was like it didn't have any power. Then all of a sudden the engine would rev, and it would go faster, and i would be able to put it in third gear, and it would work fine. but the same problem would happen again after i came to a complete stop, it wouldn't gain speed in second gear. it is the middle of winter here so it's quite cold. i've had the battery replaced recently. I thought this could be either the transmission or clutch, but wasn't sure. Do you have any advice of how i could check it? The check engine light comes on when I start it now, and I'd be nervous to drive it again

My car has 230000 miles.
My car has a manual transmission.