Made some today and it came out really horribly.
I used parmesan cheese, half and half, milk.

I mixed the half and half with milk and let it boil down a bit
then I added the parmesan cheese

Yeah--that would. You either need to use cream instead of milk and half and half for the American version, or cut out any liquid but some pasta water you reserve after coking the pasta for the true Italian version.

First of all there's no "real" italian version as this is a very "americanized" italian meal...
And yeah when you make sauces, reducing down milk is not an option... you either want to go with heavy cream, or if you use milk you will have to thicken it up with butter/flour (roux) ... but thats not really "alfredo"... alfredo is basically reduced heavy cream with parmegianno...
If you want a more flavourful sauce, you can start by sweating shallots with a bit of garlic slowly (no color) then deglaze with just a bit of white wine, then add heavy cream, let boil for like 1 min (or until its thick enough) then throw in parmegianno...

Also, the 'sauce' was too clumpy.
Like the cheese didn't melt or something.
I used shredded parmesan.

Should I use a different kind of parmesan?
I'll try with cream next time.

Hmm...that will be news to my Italian friend. And also the Alfredo restaurant in Italy where it was invented. I did forget to mention you need butter in the Italian version.

I've worked with italians from Rome and nobody knows what alfredo is there.... also what you're referring to is fettucine al burro, which is an italian classic... alfredo is like a variation from the classic fettucine al burro..

"Fettuccine Alfredo has now become ubiquitous in Italian-style restaurants in the United States. In Italy and throughout Europe, the name "Fettuccine Alfredo" is basically unknown. In Rome it is usually called Fettuccine al burro.[7]"

you forgot the nutmeg, salt, pepper, heavy whipping cream and butter.

It's one thing to be ignorant and caught in a mistake, quite another to be pompous about it. Your point that real Italian fettuccine Alfredo is a variation on a classic dish is--what do you know--exactly what my point was. And guess what--my friend from Florence taught me the dish. If you'd stop trying to pretend you know more about food than everybody else we might actually get some decent conversation in here. Your Wikipedia source even leads off with:

"Fettuccine Alfredo is a pasta dish made from fettuccine pasta tossed with Parmesan cheese and butter.[1] As the cheese melts, it emulsifies the liquids to form a smooth and rich coating on the pasta. It was named by an Italian restaurateur at his restaurant Alfredo on the Via della Scrofa in Rome in 1914."

Alright so what's the game plan for when I make alfredo sauce next?

Heavy cream (not half and half cream, right?)
Parmesan (should I continue to use shredded? I don't know where to get real parmesan)