Alright my 99' SSEi is throwing 2 error codes right now.

The first one being P0203. From my research that means:

The second one is P0303:
Now I just recently changed my spark plugs and wires and the code remains.

Anyone know 1. If this is something I can fix myself and 2. How/what do I need to do to fix this.

I'm unsure of your mechanical ability, but this is a reasonably easy item to fix.

First off is the diagnosis. The description code you gave us says there is a problem with the #3 cylinder injector. That is backed up by the code for #3 cylinder misfiring or not firing. #3 is the middle cylinder on the front or radiator side of the motor.

Diagnosis:
1. Review the wiring going to the injector for any obvious defects or problems.
2. Remove the connector off the injector and put the tabs from a 194 (front blinker) light bulb into the connectors. One tab into each connector. Start the car and observe the light bulb. Does it flash? If yes, got to step 3, if no step 4.
3. All your indications show the injector to be bad or plugged. It will need to be replaced. Local parts stores sell them, but so do many junkyards and other folks on this forum may have one they'd send you.
4. Oh crap, it'* a wiing or pcm issue. We'll need to dig further.

Ok..that'll get you started. C'mon back and let us know if you are a 3 or a 4.