Learn English – I don’t know how to feel about it/I don’t know what to feel about it

Because doubt is an old word (the OED attests it from 1225) there are a number of nuances of meaning. In summary, with my numbers not OED's:

1. A subjective state of uncertainty about the truth or reality of something;
2. (plural) A feeling of uncertainty as to something;
3. The condition of being objectively uncertain;
4. A state of affairs which gives rise to uncertainty;
5. A matter or point involved in uncertainty; a difficulty (Obsolete);
6. Apprehension, dread, fear (Obsolete);
7. A thing to be dreaded; danger, risk (Obsolete).

As a singular noun, it is decidedly abstract and refers to a state of being. Thus one can be in doubt about something. As a mass noun referring to a state of being, doubt would not normally be pluralised.

When it refers to a particular feeling of uncertainty it is pluralised. Thus if one has that feeling, one has doubts. One does not "have a doubt" because the singular doubt refers to a state of being; senses 5, 6 and 7 which refer to particular things are obsolete in Standard English.

The uses which are obsolete in Standard English may have survived or been resurrected in other dialects. The ELU references say that it does occur in Indian English.

The relationships between men and women (boys and girls) can be confusing regardless of how careful you are with language. "I like your hat," could make some people clingy and desperate with a possessive infatuation. Currently, the expression, I have taken a shine to you seems to exist somewhere between, "I'm impressed," and "I think I love you."

take a shine to somebody (Cambridge Idioms Dictionary, 2nd ed. Copyright © Cambridge University Press 2006. Reproduced with permission.)

(informal)

to like someone immediately

I think Andrew has taken a bit of a shine to our new member of staff.

The etymology of shine:

1520s, "brightness," from shine (v.).

Meaning "polish given to a pair of boots" is from 1871.

Derogatory meaning "black person" is from 1908 (perhaps from glossiness of skin or, on another guess, from frequent employment as shoeshines).

Phrase to take a shine to "fancy" is American English slang from 1839, perhaps from shine up to "attempt to please as a suitor."

Shiner is from late 14c. as "something that shines;" sense of "black eye" first recorded 1904.

Particularly in it's early usage the expression implied a romantic interest.

High life in New York, by Jonathan Slick, 1844:

If she wanted to take a shine to a Yankee, why couldn't she a found a feller worth a looking at ? But sometimes it does seem as if these gals couldn't tell bran when the bag's open — the brightest on 'em.

Dictionary of Americanism. - New-York, Bartlett 1848:

SHINE. To take a shine to a person, is to take a fancy to him or her.

SHINE. To cut or make a shine, is to make a great display.

*All the boys and gals were going to camp-meetin'; so, to make a shine with Sally, I took her a new parasol.*

The Knickerbocker, 1864:

'it 's rare to see a feller take a shine to a woman old enough to be his granmarm, but...

There were also times it was used without romantic implications, as in a 1900 edition of The American Magazine:

That's what makes it so ticklish dealin' with Indians; you can't tell what they're thinkin', by their faces, any more 'n you can a clock. But when they take a shine to a feller, they don't ask no questions.

A Dictionary of Slang, Jargon & Cant, 1890:

to take a shine, to be partial to a person or thing, to take a fancy

In 1898, the expression was used with the implications of "first impression", in The Deserter, and Other Stories:

... That's what made me take a shine to you, right off.

and in The Outlook - Volume 60:

Later he explained the matter to the teacher. "I didn't take a shine to you nohow this morning," he said ; " I thought you was one of these here psalm-singing gospel fellows, and I ain't got no use for that kind. But when I seen you setting up there and a-eating pie with a fork, I changed my mind. I knowed right away you was a gambler."

More recently the same range of meanings prevails. A Bride for Noah, 2013:

Uncle Miles, who had remained quiet until now, stepped forward. “It seems some of our Indian friends have taken a shine to the ladies and have taken steps to proclaim their feelings.”

Wild Animals and Wedding Outfits, 2013:

The Captain seems to have taken a shine to Bill's repertoire and keeps exhorting him, 'Mr William, Mr William, give us a song!'

The Oxford Thesaurus of English, 2009, seems to have landed on the romantic implications, including it among various substitutes for fancy:

2 she'd fancied him for ages: be attracted to, find attractive, be captivated by, be infatuated with, be taken with, desire; lust after, burn for; informal have taken a shine to, have a crush on, have the hots for, be wild/mad/crazy about ...

Realizing the historically strong implications of the phrase, the strong potential of misunderstanding between men and women, and your desire to prevent a possessive infatuation, it seems wise to avoid this expression.