Please help!!

Can I break my lease if I have rats in my apartment? And I have a child with asthma? This in the state of Florida?

Just having a rat in the apartment is not grounds for breaking a lease. Sorry but your child's illness is also not grounds for breaking a lease. You need to report the problem to the owner or management and allow them reasonable time to cure the problem. If the problem goes unaddressed you might consult a Florida attorney about hiring a contractor and then deducting the cost from your rent or sueing for the cost. Do not do anything that will hurt your standing down the road such as withholding the rent now when you are just reporting the issue.