Should having sex the second time still hurt?

It could. Depends on many factors, you should see your obgyn so he or she can do an exam to see if any of the hymen ring is still intact or if you have a cut or tear or tissue irritation or your partner could be too rough or other conditions that your doc can diagnose.
It can. Pain can come from lots of sources, ie too hard, too long, too dry, vagina too tight, penis too big, not enough foreplay, etc. Good sex takes practice! use extra lubrication, go slow, spend more time during foreplay. If things start to hurt, slow down or stop, cuddle and try again later. It gets better, but it takes time and practice and a gentle (and skilled) partner!