Try different ways of drinking it. A Whiskey Connoisseur will tell you the only way to drink it is neat (without any mixer or ice), so give that a try, just pour out a small glass and sip it slowly. If you don't like it immediately, give it time and see if it grows on you.
If not, add some ice and see if you like it cold.
If not, try mixing it with coke. A ratio of roughly 5:1 is reasonable, then adjust to taste.
Most alcoholic drinks are acquired tastes, and whiskey particularly so (in my opinion) so don't be surprised if you don't like it. Also, if you don't like it, don't decide that you just "don't like alcohol full stop." there's a massive variety of different alcoholic drinks to try.
You may not like the taste, but there will probably be no problem swallowing it and keeping it down if your only sipping it. There's no reason why it should make you throw up unless you get really very drunk.
To avoid getting drunk, just drink it slowly and stop when you start notice yourself become a little uncoordinated, and a faintly warm and fuzzy feeling through your whole body. This is the time to stop drinking, unless you mean to become drunk.
Take particular care if you mix it with coke- it is much easier to drink and you may find you drink it faster than you mean to.