Welcome to HEALTHCARE MAGIC..
I have gone through your query and can understand your concerns....
As per your complain feeling of lump in throat and continuous burping seems to be due to Acid reflux and inflammation of the lining of throat due to injury with acid can cause swelling and feeling of something stuck in throat..
Sore gums and spitting up of blood while cleaning teeth can be due to either gum infection
and inflammation or can be due to gum Inflammation
secondary to Acid injury..
I would suggest you to consult a Gastroenterologist
and get evaluated and an Upper G. I Endoscopy can be diagnostic..
For acid reflux Proton pump inhibitor like Pantoprazole , antacid like Milk of Magnesia
or Calcium carbonate
, small frequent meals, weight loss and moderate workout, eating dinner 2 hours before sleeping and drink plenty of water can be advised..
For gum Inflammation if it is due to infection consult an Oral Physician and get Scaling done followed by gum paint application over gums..
Hope this information helps..
Thanks and regards.
Dr.Honey Nandwani Arora..