If I get bit by a mouse will I get sick?

The odds of getting bitten by a mouse are less than the odds of getting stuck by lightening.  Mice do not bite in self-defense.  They play dead or run.  The species of mice that carry Lyme are not the ones that typically in habit houses, so encountering an infected mouse is unlikely unless you intentionally try to capture live mice outdoors.

Otherwise, Borellia is likely to be present in the saliva of an infected mouse, so if you went out of your way to capture a live mouse infected with Borrelia and somehow got the mouse to bite you and also got saliva into the wound, then maybe you could end up with Lyme disease. 

You must consult a doctor since getting bit by mouse can cause serious health issues

Lyme disease comes from the TICKS on the mice. You can only get it from a tick bite, not a mouse bite.

I have been bitten by numerous mice without getting sick.  And yeah, I mean wild mice.  Pet mice don't bite that often, but as I love rodents, I have captured and handled plenty of wild mice and rats.  Been bitten by rats too.

I never heard of anybody getting Lyme disease from a rodent.  People get it from infected ticks. Which is very different, because a tick inserts its proboscis into your skin, injects some anticoagulant, and stays there for many hours if you don't take it off.  If you get the tick out of you within 12 hours or so, it is not considered a risk for Lyme.  So, a mouse bite is not going to pose a risk for Lyme.

BTW, is it racist that they named the illness Lyme disease?

I don't know how much your health teacher knows, but you know, different species of mice tend to carry different diseases.  In the country, there can be different species of mice.  House mice, deer mice, white footed mice, harvest mice - to name a few.  And then there are voles that are often called mice.  I actually live in town, but the only mice I get are harvest mice.  Most people don't know the difference.  

Mice are frightened of humans. You may only get bitten if you picked up a wild mouse.