Hi,
1)shoes...could be cheap shoes, or just the wrong shoe for you. I love my Sidi
Dominators, but they were very expensive
2)socks...try this
http://www.sockcompany.com/wrigdoublayr1.html
The best cycling sock I know of is by Smartwool; but these require hand washing and then you dry them by hanging them up. And you never, ever, wring the water out. A pain to wash, but they are heavenly.
http://www.sockcompany.com/smarxteamrac.html\
If you have the room in the shoe,this might be even better...
http://www.sockcompany.com/smarrbxulcus.html
3) innersoles.....there are dozens, many good, I am using Superfeet. Try a few, you might get lucky.
4) Your feet swell as the day progresses. They swell more cycling, on top of everything else.... I just reach down and loosen the velcro straps. If you have
shoelaces, loosen them. Doing just this should help, at least a little.
5) Old hiking trick I have been meaning to apply to cycling. bring a spare pair (or two) of socks, and a little talc (there are some expensive powders that are nice, I have been trying Rebound). Stop for a couple minutes every hour, put the cool socks on, and throw a little talc in. A dunk in a stream is ideal, but not too likely.
6) If the situation has gotten quite bad, you might need to see a foot doctor.
I am told a metarsal bump helps some people; but I haven't tried that