I wrote a really, really, good short story recently, with an amazing main character. I want to use her again, but it doesn't feel right to put a character from a short story into a long series! should I write a series of short stories about her?
If you're wanting to go with a longer story like a novel, I'd suggest either making your short story in the past (of the longer story) or announce that the short story isn't canon (doesn't effect or make anything different for the main story).
A series of short stories would also be cool, but that decision is entirely up to you! :)
The problem with short stories as compared to novels is that they usually just show an aspect of a person's life, without digging too deep into the backstory of the character. While it is absolutely possible to convert a character from a short story to a novel form, I do believe that it might be necessary to provide more backstory.
Thus it would probably change the way we experience it. It will be a more episodic story telling which might not go hand in hand with the (traditional) understanding of short stories.
(Of course, anything that one can think of is possible, do not let traditions stand in your way of your creativity, enjoy the process and have fun with it.)
Many short stories have been turned into novels
Flowers for Algernon by Daniel Keyes was a short story that was then adapted into a full novel. M. R. Carey turned Iphigenia In Aulis into The Girl with All the Gifts. Dragonflight, the first book of Anne McCaffery's Dragonriders of Pern began life as two novellas, Weyr Search and Dragonrider.
In all of these cases and more, the longer novel stands adjacent to the original stories. The story told in the short story is repeated in the novels, although sometimes with details changed to better fit the longer form story being told.
A second form of adaptation can be seen in Seanan McGuire's novella Rolling in the Deep, which was followed by the novel Into the Drowning Deep, and Mary Robinette Kowal's The Lady Astronaut of Mars, which served as foundation for The Calculating Stars and The Fated Sky. This sounds a bit more like what you're interested in. The original story is part of the canon of the world, and the novels are additional stories in that world. Kowal's series even features the same character!
And there are also many novels that began life as short story collections. Callahan's Crosstime Saloon by Spider Robinson was a series of short stories collected together, as was I, Robot by Issac Asimov, and Sparrow Hill Road by Seanan McGuire. Collecting stories together like this does leave a mark, though. It is usually fairly easy to tell when a story began life as a short story collection. (In particular it is educational to look at Sparrow Hill Road, which began as a short story collection, and its sequel The Girl in the Green Silk Gown, which did not). That is not necessarily a bad thing. Many people enjoy the episodic feel of a novel made of short stories, and some stories are best told in that manner. It's like writing a TV show instead of a movie. Both are excellent storytelling mediums, but they are also different storytelling mediums.
The path you choose is up to you. All paths are equally valid, but the considerations you need to make for each one are different.