There are only a few possible healing problems associated with tattooing. The first obvious one is infection. Tattoos can be red or irritated, but infection is a green or brown discharge. Infections do not come out from shops, usually the client has gotten into something they should not have or just not taken care of the tattoo. If you see a tattoo get infected, you should ask what the client is using for the care. Rubbing alcohol and peroxide will only make the infection worse. Rubbing alcohol will dry the skin out causing it to heal harder and peroxide will eat away the infection and the new skin growing back.
The worst thing you can do on an infected tattoo is any kind of salve. The salve or ointment will seal in the infection and cause it to get much worse. You instead, need to dry out the infection. The best thing you can tell your client is to only wash the tattoo two or three times ad day for two days. If the infection gets better, then keep it up till the tattoo heals completely. If the infection stays the same or gets worse, then you need to tell them to go to the hospital where they will flush the wound and put them on antibiotics.
Never diagnose an infection over the phone. Tell your client that they must come in, for you to see the tattoo first hand. If it is already progressed then you need to tell them to visit their doctor. Most of the time it will just be red or sore to the touch and people just assume its infected. Everyone loves to panic.
Allergic reactions are common at the tattoo field. If someone has an allergic reaction to a tattoo then best bet is that it will not be the pigment. Again, find out what they are using for aftercare. Most of the time, the culprit will be lotion with perfume in it or made for tattoo aftercare. Symptoms of allergic reaction are small red bumps around the tattoo, the surrounding area of the tattoo can be red in color, the tattoo will be more painful than usual, and sometimes you will see a clear or white discharge.
The best thing you can do is tell them to discontinue the aftercare they are using and wash the tattoo in antibacterial soap to kill the bacteria so it does not turn to infection. If it progresses into infection then follow the instructions above. Do not tattoo on diabetics unless you know them personally. Diabetics are more open to infection due to the lack of circulation associated with the condition. This means the tattoo will heal much slower on top of being higher risk for infection. Remember that the over all health of your client is infinitely more important than the outcome of the work. You can always touch up a tattoo after it heals. Do not take any risks.