IPL Side Effects from Melasma Treatment

You have two different issues going on. The striping on one cheek sounds different from the coffee stain on the other. The striping sounds like hyperpigmentation (brown discoloration caused by the trauma of the treatment) and the coffee stain sounds like your Melasma is showing up more clearly.
The IPL will only make your Melasma worse. We are not sure why your practitioner used an IPL for the treatment as it is not FDA approved and most if not all light based devices will make Melasma worse.
The striping you see is caused by a treatment where the energy level is too high. When this happens, the heat of the device focuses at the surface of the skin rather than lower levels, causing blisters or burns.
DO NOT have another IPL treatment from this practitioner as they do not know what they are doing! Find an experienced practitioner that can help you solve the problems that you now have. Hydroquinone bleaching creams are a good option for both problems. And do everything you can to avoid the sun as this will delay the healing process and worsen your Melasma.

IPL can leave discoloration and is not very effective on treating melasma.Darker skin people are not good candidates for IPL and often two weeks is not enough time for the tan to fades.Melasma can succesfully be treated mith Fraxel restore laser and pretreating the skin with hydroquinone, or bleaching cream improves the results.IPL seems to be working better for sundamaged skin or broken blood vessels on the face.

It is true that sun exposure can cause an unwanted response to IPL. The melanin is a chromophore for IPL meaning that it is a colored target that absorbs the light energy produced by the intense pulsed light. Too much chromophore and the skin can actually break down.
The tiger stripping is due to the actual shape of the ILP crystal. The bad news is that a "no-down time" treatment suddenly has a lot of down time. However, these will often heal completely on their own. Certainly avoid more photofacial at this particular office. Time will usually heal the stripping and one week is extremely early.
Also, be weary of treatments that claim to improve melasma. Bleaching products also tend to produce little improvement. On the other hand, if your melasma got more obvious with sun tanning, consider avoiding sun exposure, or use appropriate sun screen. This may help fade the melasma.