Trouble with 88 Camaro start

I recently purchased a 88 iroc 350 tpi, rebuilt motor approx. 8k miles on it. No problems until now. The fuel gauge pegged out at full when I filled up about 5 or 6 days ago. Last night I stopped to fill up on fuel and when I tried to restart the motor it cranked and died. I gave it some throttle a couple tries later and it fired up but needed constant throttle pressure. I eventually drove it home but could not take my foot off the gas or else it would die. I tried starting it this morning and same thing. Could it be my fuel sending unit or maybe fuel pump? I do hear the fuel pump come on. Only a 34 trouble code comes up.