My immune system has been weakened from severe stress lately, ended up getting a real deep cut on my hand yesterday from some glass, woke up today with my muscles feeling tense and my jaw feeling tight and swollen, I don't remember the last time I've had an immunization but I think it's been atleast 10 years.

yes it is possible

Unless the glass had dirt on it, tetanus is very unlikely. the bacteria lives in the soil and requires an anaerobic environment such as a deep wound to germinate. since it grows slowly, symptoms don't appear until much later.

Getting a booster wouldn't hurt though.

Also, ignore the lying antivaxxer. Tetanus rates are so low due to the vaccine. While people, like you, are often not up to date, they do get vaccinated after deep wounds.

Additionally, the vaccine often does confer protection to an new infection in an open wound. Once symptoms actually, start, it isn't very useful since the adaptive immune response takes time. Even then, it is still given.

Those opposed to vaccination typically have little to no knowledge of medicine or biology.

Yes, it is possible, but unlikely. the incubation period is usually 3 to 21 days, but may range from 1 day to several months (source, American Public Health Association Control of Communicable Diseases Manual). if you have not had a tetanus booster in more than 10 years, you should get one. Immune globulin is only used in those who have not previously received a complete series of tetanus immunization, so whether or not immune globulin would be used depends on your vaccination history.