First, never have sex if you don't want to. Boys will beg and plead, but they are being selfish if they don't think about your own feelings and discomforts.
Second, there is nothing wrong with sex during your period. It can be a little messy and he will get some blood on him, but if he can deal with it, no problem. In fact, barring any diseases, this is the safest time to have sex as the odds of getting pregnant during your period is practically nil.
But, having mentioned diseases, since there is blood involved, any blood-borne diseases can be easily transmitted. So, while birth control is not really needed, you still need to use condoms as the risks are much higer for passing something on.
If you are concerned about the mess, do it in the shower, but if not there, then as was suggested, lay out some old towels, and be sure to have a place to wash up afterwards.
Finally, though, if you don't feel good or if you are not comfortable about doing it during your period, then don't. It won't kill anyone to wait a week to have sex.
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You could also do it only on the days when your flow is lighter.
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