Don't give up yet!

It sounds like your bottom bracket (the crank axle assembly) needs to be moved over to the right (moving the crankset outwards) a bit to get the small chainring to line up better with the smaller cogs. Some bottom brackets are adjustable from side to side, and others may be able to accept shims to move them over. Check with your bike shop. If your bottom bracket isn't adjustable, you may be able to get a new, better model that is adjustable. Or, a bottom bracket in a slightly larger (wider) size may do the trick. Bottom brackets do tend to wear out every few years, so you might need a new one soon anyway.

Another thought: if you have a "spoke protector" in between your cassette and your spokes this is unnecessary for a road bike, and removing it might allow your cassette to move inwards a little bit and help with better chain alignment. Just make sure that your rear derailleur limit screws are adjusted correctly after removing the spoke protector.