I can give you a general answer to this one and it's generally the same in each state.
You are entitled to what is called "quiet enjoyment" of your apartment. Because of the barking dogs, that can be deemed to violate your quiet enjoyment and use of the apartment.
If your landlord fails to stop excessive and unreasonable noise, you may consider filing a small claims case against the landlord for creating a nuisance, although I don't recommend it if you already have anxiety. You can ask for damages there but they probably won't give you punitive damages.
Look at your lease. Look for a clause that’s called something like “violating laws or causing disturbances.” Your landlord may also spell out specific noise guidelines (such as no loud noise after midnight) in a separate set of rules and, so check these, too. Also look to see what happens if you want to end your lease early.
It’s your landlord’s responsibility to enforce lease clauses.
Depending on the situation, you may be able to break your lease and move out early. You can check your city's noise ordinance. Almost every city has noise laws that prohibit excessive and unreasonable noise (including sustained noise over a certain decibel level) and designate certain “quiet” times (such as between 10 p.m. and 7 a.m. on weekdays).
The next step is to send a letter to the landlord, registered, return receipt and keep a copy for yourself. State that he is violating the lease provision of quiet enjoyment and also state if he is violating the city noise ordinance. If your lease requires you to pay the full term of the lease if you vacate early, you're not going to refer to that in the letter. You will explain that this is a nuisance and it is interfering with the quiet enjoyment of your apartment.