Asking people not to use the word "queer" to describe you personally is a completely reasonable thing to do, but I would caution you about asking people not to use it when describing themselves.
I understand that some people are uncomfortable with the word, many people have some really rough memories tied to the word being used as a slur against them, and it's understandable that the word still carries those connotations.
So if you need to ask someone not to use it to describe you, simply explaining your experience with the word, how it makes you feel, and what words you want them to use instead, should solve the problem for you.
I mentioned that you should be cautious about asking other people to not use the word because it's a word that has been somewhat reclaimed or reappropriated
In sociology and cultural studies, reappropriation or reclamation is the cultural process by which a group reclaims terms or artifacts that were previously used in a way disparaging of that group.
It's worth mentioning that reappropriating/reclaiming a word has a way of taking its power. You're not only reclaiming the word itself, but you slowly end up taking control of its power to hurt you. Admittedly I still get pissed when people use it as a slur, but reclaiming it allows me to laugh in their face when they do. Sort of a:
That was the most hateful thing you could think to say, and it's a word me and my friends embrace. You've got nothing...
Believe it or not I have friends that use "fag" for the same reasons. Once you own it, they can't use it against you.
I personally use the word "queer" because I'm not straight, gay, or bisexual. I'm pansexual and a lot of people aren't familiar with that term. The term "queer" also feels a little more inclusive, to me personally, than a lot of the other options, because it speaks to the common experience of being ostracized and/or bashed for being different that many LGBT+ people share. Basically while LGBT+ people may not all have the same sexual orientation, we all share some similar experiences, we face many of the same hardships, and I tend to think we should come together as a community because of that, and to fight against it.
I just stumbled upon a relevant post on imgur, screen shots from a Tumblr thread where people were discussing this exact issue: https://i.stack.imgur.com/zpLpO.jpg
"Queer" apparently has a much longer history of reclamation than I originally thought. One could argue, and few folks did in that thread, that queer has been used as an umbrella term since the start of the LGBT rights movement, it significantly predates "LGBT".
A few even questioned whether it was really a reclaimed term at all. According to one source, gay men were using the term for themselves in 1910, so it's worth noting that this may have been our word to begin with and that it may have been co-opted and used as a slur later.
"We're here, we're queer, get used to it!"