Does my lawyer can take adding the med pay amount to my settlement amount?

You need to read the Agreement you signed when you retained your lawyer. If it says he is entitled to a fee out of all sums collected on your behalf, and he collected both the settlement and the medical pay, then he'd be entitled to a fee on both (although you may be able to get him to waive some of the fee or offer a reduced fee on the med pay part of the claim?) If his Agreement doesn't indicate he can charge a fee on medical pay, then he can't. If the medical pay was paid without him providing the necessary information for the insurer to make payment and they voluntarily paid it, then there may be no grounds for charging a fee thereon (again, it is typical that the Agreement would speak to this and control).

It is not unusual for the attorney to charge on the med-pay.

Your attorney's fee of 1/3 comes off the gross amount of the settlement. The remainder is to satisfy all liens and the balance going to you. It appears that he is double dipping.

If your lawyer was able to get those waivers, then he is entitled to a fee because it was part of his complete job.

You are right about your feeling that something is not right (or so it seems). But wrong about your understanding about medical pay. Normally a lawyer will not take a fee on med pay since it should be more or less automatic. Why don't you just ask your lawyer to explain. There are "waivers" you say, maybe some liens and other factors you don't know about. Talk to the lawyer and understand before you sign.

It depends on the language of the engagement agreement between you and your lawyer, but generally he should take his percentage only from money actually paid from the defendant's insurance company.

Most lawyers charge a percentage of gross recovery from all sources, including insurance proceeds from either side. Ask your lawyer about your concerns. I'm sure he or she wants you to be satisfied that he or she isn't being dishonest with you or taking advantage of you.