well,yes,wrapping it will help,put on something like Aquafor or cocoa butter under saran.
next time ,something like these dermal films below will solve that problem if you buy it before,I get mine online,
unless you can find it locally.
like Saniderm or tegaderm , you should be able to find Tegaderm at walgreens,target,or CVS
these products are great stuff for healing tattoos IMO,I have used them for a few years now with great success.
you leave it on a tattoo for a few days,you can shower and sleep with it on and no hassle.
here is some reading here on it.
and remember to keep it clean.
this is my thigh with Saniderm on it