Learn English – Term for someone worried about health after reading health information online

The verb tantalize is relevant. Wiktionary shows two senses:
• to tease (someone) by offering something desirable but keeping it out of reach
• to bait (someone) by showing something desirable but leaving them unsatisfied

Note, in the latter of those senses, bait is used to mean teasing, luring, or enticing someone with something they apparently desire, but keeping it out of their reach.

This is a noun, but such a person is a worrywart. It is frequently used to describe loved ones who are overly concerned about your well being. It fits perfectly into your example sentences.

My mother is a worrywart.

I want to tell my mother about my flight tonight, but, you know, she is a worrywart and will lose sleep worrying over my safety.

This word is very informal, but not derisive. It typically implies some measure of affection.

The expression is used mainly in American English.

Worry wart:

1956, from comic strip "Out Our Way" by U.S. cartoonist J.R. Williams (1888-1957). According to those familiar with the strip, Worry Wart was the name of a character who caused others to worry, which is the inverse of the current colloquial meaning.

(Etymonline)