Can I use HAD HAD, HAVE HAD, and HAS HAD??

The answer is YES. It is grammatically correct to do so.

Has, have and Had generally pose confusions for non-native English speakers. They are auxiliary(helping) verbs used to form sentences in the Perfect Tense, as well as stand-alone verbs to form the Simple Present tense. 

To understand about whether using them doubly, like had had, have had and has had, is correct, we will have to take a look at the present perfect and past perfect tenses.

The perfect tense always uses has / have (present) / had (past) + past participle. Click here for more information on past participles.

Here's are a couple of examples of Perfect Tense:
Eg.: Mila has done her homework. (Present Perfect)
Eg.: Mike and Molly have eaten their dinner. (Present Perfect)
Eg.: Philip had gone to the market yesterday. (Past Perfect)

We use has/have and had in Simple Tense, minus the past participle:
Eg.: I have a pet dog. (Simple Present)
Eg.: She has chicken pox, so don't go near her. (Simple Present)
Eg.: I had a pretty blue frock when I was small. (Simple Past)

When we use them to form Perfect tense sentences, for example Present Perfect tense, we can use 1 have/has + 1 had in place of the past participle, as per the rule. 
The past participle form of have and has is had.

I	have	had	a	lot	of	homework	this	week.
	Present Perfect	PP of have

He	has	had	a	lot	to	drink	tonight.
	Present Perfect	PP of has

In the same way we can use had had to form Past Perfect:

I	had	had	a	severe	cold	last	month.
	Past Perfect	PP of have

So there you go! As long as you have a Past Participle after have/has/had, you are talking in Perfect tense. If using these three verbs alone with an object, you are in the Simple Tense.