Its hard to say without seeing it but, it sounds like a polishing(2-5 steps) is needed with a high-speed buffer. Don't use a high-speed buffer if you do not know how, you'll do more damage than good.
You could do it by hand or w/ orbital buffer but, you'll only be covering the damage for a few months then its has to be done again. High-speed is the only way to remove the top layer of paint properly.
Take it to a good detail shop for their opinion. Ext. detail can range from $60 and up. Expect to pay around $125 for a quality job.
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