Word for "when someone does something good for you and then mentions it persistently afterwards"

You could use "bring up" in conjunction with "broken record" -

Bring [something] up:

To mention someone or something in conversation. A noun or pronoun can be used between "bring" and "up."

A broken record:

a damaged record that repeats part of a recording over and over again —used figuratively in describing something (such as a statement or experience) that is frequently or tediously repeated

For example,

A bought a present for me and then brought it up on every occasion [like a broken record]..

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Here's something else you can use -

Labor the point:

To talk about or emphasize something excessively and perhaps repetitively, usually to the extent that the listener becomes bored or annoyed.

If someone labours the point, they keep explaining something or emphasizing a fact even though people have already understood it.

A: "I don't mean to labor the point, but I'm just worried that there won't be enough food at the party."

B: "Yeah, we know, you've said that 10 times now."

For example,

A bought a present for me and then labored the point on every occasion..

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I also found a [Latin] phrase that could possibly fit in your scenario -

Ad nauseam [ad naw-zee-uh m]

used to refer to the fact that something has been done or repeated so often that it has become annoying or tiresome.

(Lexico)

Ad nauseam is a Latin phrase that literally means “to nausea”.

Use ad nauseam to describe something that’s been repeated or discussed so long that you’re sick of hearing about it.

(Grammarly)

: so many times that it annoys people.

(macmillan)

For example,

A bought a present for me and then brought it up ad nauseam on every occasion.

The term you want is ‘white elephant’.

He gave me a gift, and then made a white elephant of it, making me report to him on it forever afterwards. The emotional upkeep on this gift is overwhelming.

possible antidote: “It’s not a gift if I have to forever answer for how I use it.”

I have encountered at least three possibilities:

... and then brought it up on every occasion.

... and then went on about it on every occasion.

... and then harked back to it on every occasion.

Hark back = If someone harks back to something in the past, they talk about it again and again, often in a way that annoys other people

Cambridge

Go on about = To continue or speak for a tedious or exasperating length of time.

The Free Dictionary

Bring up = to start to talk about a particular subject:

“She's always bringing up her health problems.”

Cambridge

Of these three, I suggest harking back is the best, both for its defined implication of reference to the past and for its (to me anyway, perhaps because of rhyming with “bark” and “nark”) almost onomatopoeic grating aural quality.

A bought a present for me and then GLOATED OVER it on every occasion

The term "Indian Giver" or "Indian Giving" covers a gift given to you but where the giver either expects to take it back, or is expecting a quid pro quo in return.

If they keep expecting praise for their generosity, this is regarded as a quid pro quo, hence the term can cover this scenario.

Milked it for all it was worth

Free Dictionary definition

The phrase that comes to mind is banged on, which can be used in he just banged on about the gift for the rest of the day.

My guess is that this derives from banging one’s own drum.

Guilt tripping which is a form of manipulation to get someone to do something or give you emotional support or affection by making them feel guilty or obligated.

Toby Speight mentions in the White Elephant comments "emotional blackmail" which is a better description of what they are attempting to do.

never let them forget it

E.g.:

John once drove Jane to the airport as a favor, and he never let her forget it. Just the other day, twenty years later, he asked Jane to get him some coffee; saying, "Remember when I drove you to the airport? The least you can do is get me a cup of coffee."

Go on, perhaps - To talk excessively, tiresomely, or interminably (about something or at someone). (OED, Macmillan)

A bought a present for me and went on about it on every occasion.

'Harping on' is the term.

She bought me a nice gift/saved me some money/ did me a great favour - and cannot stop harping on about it.

Collins concise dictionary.

I like the "harped on" answer. You could also say "rubbed my nose in it".