Yes, most definitely anxiety can give you the feeling of a lump in the throat. It's not easy to get used to, but when you do, it will go away. Glad you have an appt. with a doctor to have it checked out. It's good to reassure yourself that everything is okay.
Before I went on medication I thought I would be weak and a loser for relying on medicine. But not anymore. I need medication just like a diabetic needs theirs. Not wanting to go on meds and seeing yourself as weak for doing so, is very common among those with anxiety/panic disorder.
Everyone is different. Some people do fine without the medication. For me, it was a matter of the quality of my days. I got tired of dealing with the anxiety everyday. Do what you think you need to do and don't feel badly about yourself! It's not your fault.