Your issue doesn't sound like your car is in Limp Home Mode. LHM is an electronic strategy to protect your transmission but allow you to get home or to a service facility. In one form you are locked in the gear you were in when LHM was activated and the engine's rpms are restricted. In the other you have only 2nd gear and reverse and your engine's rpms are also restricted.

If your engine is unable to develop full power, there are several possibilities. From restricted fuel delivery (as mentioned) to restricted exhaust gas flow. Beside the fuel filter (you can have the fuel pressure at the rail measured), you could have a collapsed catalytic convertor blocking exhaust gas from full flow. Bad O2 sensors and MAF sensors usually trigger codes but not always a MIL (CEL). You might want to scan with an OBD II scanner to see if there are any pending codes. Also, your coils, plug wires and plugs could be an issue. Or maybe a combination of a little bit of all of the above. Finally, bad gas? If you use one station regularly, try a different one for a few tankfuls and see it there's any change.

I'm afraid you'll have to do some detective work (analysis) to sort it out.

Good luck.