have a hangover (feeling physically sick the day after drinking alcohol)

Example 1: I went out last night and now I have a terrible hangover.

Example 2: Do you have any special tricks for getting over a hangover?

Example 3: Last night I thought I could never get enough of that wine, but today I have a hangover.

be hungover (suffering from a hangover after drinking alcohol; tired and ill in the morning because you drank too much alcohol the night before) — страдать от похмелья; с похмелья
Also spelled hung-over or hung over

..... You look distinctly hung-over.
..... Many people drink a Bloody Mary (a drink with vodka and tomato juice) when they’re hungover.

the morning after (the night before) (=the effects of drinking liquor or staying up late as felt the next morning; the feelings associated with having drunk too much alcohola; a hangover) — похмелье; «после вчерашнего»

Example : Frank's got a bad case of the morning after. (thefreedictionary.com)

Example: She's suffering from the morning after the night before. (thefreedictionary.com)

Example : Do worries about the morning after keep you from having a good time at parties? (thefreedictionary.com)

a head (a hangover)
Usage note: always with a in this sense.

Example: How do you get rid of a head so you can go to work?

brown bottle flu (a hangover or sickness from drinking)
{Probably from beer, which is often sold in brown bottles.}

Example: Wayne had a case of the brown bottle flu and didn’t make the meeting. (McGraw-Hill’s Essential American Slang Dictionary)

blue flu (a hangover)

Example: He was out late last night and has the blue flu. (McGraw-Hill’s Essential American Slang Dictionary)

bottleache (a hangover; the delirium tremens)

Example: I got a touch of the bottleache this morning. (McGraw-Hill’s Essential American Slang Dictionary)

Related entries:
опохмеляться =>
[hair of the dog]
(with a) thick head