This is straight from the local Tattoo guy in my area, He just did mine and its what Im using/doing to keep it clean.
1.Leave the bandage on for at least 2 hours. If this means leaving it on overnight be warned it may come off in your sleep so wear an old t-shirt. If you wake and you find your bandage has actually come off and you are stuck to the t-shirt then be very gentle separating yourself. It can help you wet the t-shirt.
2.Wash the tattoo once you have taken off the bandage and do not replace. It needs air to breathe! Use just water and very mild soap to get of bits of blood but be gentle – don’t scrub it.
3.Moisturise every couple of hours or whenever it begins to feel slightly dry from now on. It’s important to use a non scented moisturiser, ones without alcohol and simple ingredients work better in general. There is no need to use antibiotic cream or lotion unless you get an infection.
4.Wash your tattoo several times a day for at least 5 days. However, don’t submerge it in water. Be careful of it in the shower or bath and definitely no swimming.
5.Limit your exposure to the sun. Use plenty of sunblock when you are outside then once it has healed you should try and cover it when are are outside for a long period of time in intense heat.
Wait about two weeks for it to heal entirely. If looked after correctly everything should go smoothly and your tattoo will be bright and virbrant for a long time. However, expect to start fading over time.
TIPS: Talk to the person who did your tattoo because the aftercare depends on how the process was carried out.
Always wash your hands before touching your new tattoo.
After washing it, dry with paper towel because they are more sanitary and can be thrown away and a clean one used next time. Don’t rub – always pat dry.
On the first day sprinkle your bed or night clothes in baby powder to try and avoid sticking.
Have showers instead of baths (unless your tattoo is on your should for example and you feel you can keep it dry). Don’t let the shower spray directly onto your tattoo though.

WARNINGS: Do not scrub, scratch or peel your tattoo.
Only use NON-scented mousturiser.
Don’t use antibiotics unless necessary as it could make them less effective in the future should you need them (for your tattoo or anything else).
While healing, don’t shave where your tattoo is.
Dispose of old bandages properly as they will attract germs.

So anyway the answer your looking for is Bacitracian, NO neosporin it tends to draw out the pigments out. Also NO petrolum or vaseline based product.Also letting the shower run directly on it isnt a good idea either.Deaden if you can find it works for numbing against the pain, and if you get another one ask the artist to use it to help numb the location a bit. My friend says he uses it on alot of his customers as it helps them tolerate it better if they have a low threshold for pain.
I hope this answers your question sorry its a long answer though. Nites

I used good old fashioned nappy rash cream on my tatts. In Australia it’s called Bepanthen cream. My tattooist said the main use of using a cream was to keep the wound (tatt) moist so that it didn’t scab too much and possibly loose some ink colour. Infection wasn’t an issue but she did recommend a cream called Savlon (in Australia anyway) if I was worried at all.