Word for a small short cylindrical glass container (for salves, creams etc.)

There is no height limit on a jar. I have several in my fridge that are less than an inch high and some are several inches wide.

It is perfectly fine to call a small container made of glass or ceramic a jar.

I make salves, so I often buy containers online. Most websites call a short jar a "squat jar." It usually has a wide mouth in comparison to its height. Here's a picture of one in an online shop.

Another word for such a container is a tub.

A tin doesn't necessarily have to have a lid, so I would call a container as you describe it "a glass".

The first thing that comes to my mind is a vial.

A dram might work - generally refers to a specific quantity, but it has its origins in pharmaceutical products, and was a common size small jar for selling medicine or other similar products.

The possibly-appropriate word vial has already been suggested, but I think phial, "glass vessel or bottle, especially a small bottle for medicines", is a better choice for fantasy fiction. Also consider ampoule, flask, and cuvette, "a small vessel with at least two flat and transparent sides".

Also note a number of related words that appear in a passage in Chapter 9 of The Nursing Home Murders by Ngaio Marsh:

"...Now I understand that the jar, bottle, or pot containing the serum—"

"It was an ampoule," said Jane.

"So it was—and the pipkin, cruse, or pottle containing hyoscine were on the table. ..."

From en.wiktionary, jar in sense 2 means "A small, approximately cylindrical container, normally made of clay or glass, for holding fruit, preserves, etc., or for ornamental purposes. ... Synonyms: cruse, pot".

From en.wiktionary, bottle means "A container, typically made of glass or plastic and having a tapered neck, used primarily for holding liquids". [Many bottles have straight rather than tapered sides. Certain metal containers are referred to as water bottles, fuel bottles, etc.]

From en.wiktionary, pipkin means "A small earthen pot".

From en.wiktionary, cruse means "A small jar used to hold liquid, such as oil or water".

Per en.wiktionary, pottle means "A small pot or other receptacle, e.g. for strawberries".

Have a look at The Free Dictionary's thesaurus here.

If you scroll down you will find a listing provided by wordnet that looks like this:

Where I come from, it's a bottle if it's narrow and a jar if it's wide.

For your purposes, I also like the above suggestion vial.

A glass is something you drink out of, a pot is big and usually for cooking, and a tub is even bigger and usually for washing. They're great words, but I don't think they're what you want.