Will a venous ulcer heal on its own?

Waiting is the cheapest-looking choice, which is why this question deserves a direct answer before any price comes up.

No, according to this source

my.clevelandclinic.org states plainly that venous ulcers do not heal on their own. The same source adds that venous ulcers can take several months to heal.

Why waiting is a poor plan

The same source warns that the damage can spread or cause infections that can become life- or limb-threatening, such as gangrene. Those lines describe risk, not what will happen to you. They are still reason enough not to wait for a sore to close by itself.

Further reading is available. A medical encyclopedia entry on stasis dermatitis and ulcers and one on venous insufficiency cover the basics. Cleveland Clinic's venous disease overview and its page on chronic venous insufficiency add causes and treatment.

What to do next in Des Plaines

Have a clinician look at the sore soon rather than after you have compared prices. Once it has been examined, ask for the plan in writing and ask which parts of it are covered by the figure you were given. That question separates a firm quote from a ballpark.

What this page cannot decide for you

A published statement about ulcers in general cannot say how yours should be treated or how long it will take. Only an exam can.