This depends partially on the cooking technique and the shrimp variety/size (=> thickness of the shell).
If the shrimp is deep fried the shell can turn crispy and is super fun to eat.
However, if boiled, the shells are chewy and extremely unpleasant - in this case you have to peel them.
I am not familiar with the spicy garlic shrimp, but you can just try if the shell is crunchy, is pleasant to eat, and does not require excessive painful chewing - go for it, if not return to your old practice of pealing it and just licking the flavoring of the shells.
cooking.stackexchange.com/users/19334/BobbyZ
The shells are edible (no harm would come to you) but unpleasant.
You're supposed to remove the shell and eat the shrimp.
If no no one is looking I'll suck on the shells because they do have nice flavor.
If you can save a decent sized pile of them, you can make a pretty serviceable broth by boiling them for a couple of minutes, but that is usually done with raw shells.
cooking.stackexchange.com/users/20183/Jolenealaska
I'm Chinese American and when I order garlic shrimp I prefer to eat the little feet beneath the abdomen because it's slightly crunchy and thoroughly marinated in sauce.
But I always peel off the rest of the shell since it's hard to chew and usually tough.
A couple of years ago I went to an Indonesian restaurant in New York City and tried a dish where the shrimp had been flash fried in extremely high heat, so the shell was thin, brittle, and edible.
The dish was called Nasi Goreng Sambal Udang Petai, or Shrimp with Stink Beans and Rice.
I won't go into the unusual beans, which deserve its own StackExchange question, but the shrimp had been fried so that the shell nearly disintegrates when you bite into the shrimp.
I found the shrimp shell to be incredibly delicious and ever since then I've tried try to eat shrimp shells if they're not too tough.
So, yes, shrimp shells are edible and, based on recent scientific research, may also provide health benefits, like lowering cholesterol and improving cartilage and joint health.
cooking.stackexchange.com/users/26848/MNRC
My wife is from China (Northeast) and she ALWAYS eats the shrimp (fried) with the shells intact.
(chopsticks, fork, hands, whatever) I do too now, and prefer it that way.
cooking.stackexchange.com/users/26502/Tim
You're supposed to eat the shrimp with chopsticks, picking one up from the platter, bite off a piece if they're large, chewing up the whole thing, and swallowing only the meat and spitting out the shells as politely as you can on the table.
I'm going to guess that if you are served shrimp prepared in this way, the shrimp are probably large.
The purpose of this method of preparation is to cook the shrimp without toughing it up.
cooking.stackexchange.com/users/24430/user24430
My brother in law is from Bangladesh and he's making beautiful prawn curries and dishes with shells still intact.
So when it comes to eating we all eat the prawns iwth the shell and head.
It's super yummie and crunchy from the outside and soft from the inside.
Try it, when grilled prawns taste great with their shells still intact.
cooking.stackexchange.com/users/34350/anke
The fact is that the Prawn/shrimp shell/skin is edible item.
But it depends only on how the item is cooked.
If you cook a plain Prawn/shrimp in an electric oven at higher degree for longer duration(try your own by trial & error way the temp & time, also other way of frying/putting on direct fire/grill helps), no matter how big it is, you can enjoy eating them whole with excellent taste.
This way you get more calcium and other minerals and their benefits too.
But it is not advisable to eat the shells if they don't get to powder form while biting (generally other ways of cooking has this problem).
It may even upset your stomach.
cooking.stackexchange.com/users/50605/veera
Shrimp shells are edible but what she said they are not pleasant.
Shrimp skin is very healthy and have a lot of health benefits like it can help you lower blood pressure and lose weight easily.
cooking.stackexchange.com/users/49966/Chris
Some Chinese shrimp dishes like the spicy garlic shrimp is served with the shell still on but head removed.  Since the shell was on during cooking, the seasoning is all over it.  Are you supposed to eat the whole shrimp with the shell, or remove the shell and only eat the meat?  I usually taste the seasoning on the shell and then peel it away to eat the meat only.
Are cooked shrimp shells edible?
cooking.stackexchange.com
<shrimp><shellfish>
cooking.stackexchange.com/questions/37086
cooking.stackexchange.com/users/4811/Thierry Lam
This depends on the variety as well as the type of cooking. Grilled or deep fried shrimp taste good with the shell, but boiled shells are chewy rather than brittle. Many people consider shrimp shells edible, especially when the shrimp have been fried and the shell is crunchy. However, some people find them unpleasant and prefer to peel shrimp or spit out the shell. However, shrimp shells are actually good for you and have health benefits.
Eating the shrimp shell as well as the meat depends on the cooking methods: eat the shell when fried not when boiled. Shrimp shells are edible but unpleasant. Shrimp shells are not only edible, they are also good for you. The correct way to eat shrimp is to take a bite, swallow the meat and spit out the shell.