Had a cough all day, but now chest is tight, itchy throat, and trouble breathing. I feel weak. Anxiety from being sick or something else?

Seek treatment. You should be evaluated. If you have a respiratory infection with difficulty breathing, it could get worse and you may benefit from a breathing treatment to open the airways in the chest. Sometimes a cold with bad cough can also trigger asthma, or "twitchy" airways and can make it hard to breathe. It could be anxiety, but that should be considered after these other possibilities.
Asthma attack? Sounds like a viral respiratory tract infection with possible asthma attack (?)... Go to see you primary care doctor asap.