Hey Michelle - I can say with confidence that your secretions are not causing the sores - saliva is nature's best method for cleaning our mouths! You mentioned that you're working with PT on your swallow - if you've been cleared of aspiration risk then you should swallow, swallow, swallow!!!
Water - all - day- long!
Swallowing your own saliva and drinking a cup of water a day is not enough action to keep those swallowing muscles moving as they should. Make drinking water throughout the day part of your home exercise program- the longer you go without eating and drinking throughout the day the longer it will take to get back to eating once your sores clear- talk to your PT if he/she is the professional helping you progress with your swallow - you need step by step treatment to move forward - your instincts are right - you do need to be doing something - right now it's drinking water, soon it will be much more - just take one step at a time!
One more thing - we all swallow our own saliva as a reflex without thinking about it - several times a minute - we oral cancer kids get that reflex all out of sync - we swallow less often which can create an odd environment in our mouths which can lead to mucous, excess saliva, thrush, etc. Swallowing cleans the mouth - the more you do it the better - mucous, saliva, water- swallow it! You may find that the mucous diminishes a bit once you start swallowing more routinely.