Hot towel bro...Trust me. I'm in the process of healing my latest ink and it's the only way to go. Do it early and often.... Here's how it works.
Once you get home and get the wrap off your new ink; run hot tap water (as hot as you can handle) on a towel or wash cloth and ring it out almost completely. While the cloth is still plenty hot put it over your ink and apply pressure. It's gonna sting a bit, but won't hurt nearly as much as your tat did.
The wrap is going to cool very quickly, so you'll probably want to warm it up and repeat the process 2-3 times in succession. You can do this as often as you like, the more the better. It'll keep you tattoo from itching as it heals and you'll barely scab up at all.
For the first day or two cover the tat with a like layer of vasoline or A&D (which I prefer) and be sure to dab off the excess with a paper towel. Be sure to cover it with the same before you take a shower, and keep the showers short.
After the first day or two switch over to lotion. Keep using the hot towel until it heals up good.
The older ink I've had done took a week to 10 day to heal up good. My last to using this method took 5-7 days max.