Burning sensation in throat and chest when eating or drinking for almost a week. Getting harder to swallow and chest feels tight. Advise please?

You need to be seen. If you are previously healthy, this suggests that something may be stuck down there that is being irritated by anything you eat or drink. Meanwhile, try an antacid, eat bulky foods like soft bread, and if you can get them, ask pharmacist for a proton pump inhibitor.
Plan. Possibly you have a viral pharyngitis. You can try over the counter medications as lbuprofen /Advil 3 times a day, hot tea, lemon, honey. For more medications you need to make appointment with doctor. .