How long will I have a burning sense in skin? Why did I get bruise patches on my hips and shoulders? (photo)

Thank you for sharing your question and photographs.  Most likely you received bruising from blood rundown from your chest as a portion of your procedure, probably the liposuction.  These should improve spontaneously with time as the bruising resolves, somewhere on the order of 2 weeks.  I would recommend wearing compression for at least a month's time to help limit swelling, and improve your discomfort.  Hope this helps.

Hello,
It seems from the picture posted that you had large size gynaecomastia which was treated by surgical removal and additionally in the beginning liposuction was carried out to remove the fat that was covering the glandular tissue.
In which case bruising over the chest and around can sometime happen like in your case.
I normally advice Arnica pills and cream (A homeopathic medications) to come out of this yellowish discoloration that takes up to 6 weeks to return to normal.
I wish you all the best.