Hello,
Thanks for the query.
First you need to treat the 
allergic reaction.
This can be done by application of mild 
steroid cream like 
desonide.
Once the 
allergy is gone you can use a skin lightening cream.
This hyper pigmentation can be removed by using skin lightening creams.
Various creams are available like melalite xl, lookbrite, Lumaglow etc.
You can take any of them.
The following should be procedure to use it.
1. Wash your face in evening around 7.
2. Dry face and apply cream all over your face.
3. Keep it for one hour.
4. Wash face again.
5. Apply some moisturising cream and sleep.
6. In morning apply a sunscreen with spf at least 30.
Do this for a month, you will see the results.
Let me know if you have any other doubts.
Thank you