Speech problems after lip fillers - ill this go away on its own over time?

Thank you so much for your question. 
You are describing an extremely unusual situation one of which I have not frankly encountered. I suspect most of your issues are secondary to swelling though it is difficult to see without a photo. I would recommend making an appointment with whomever performed your procedure to discus your situation. 

Thank you for your question. 

I encourage you to return to your injector for an evaluation to rule out any allergic reaction. If your tongue is actually swollen that would be a concern. It's hard to determine solely from your description but it may be that you are still experiencing some swelling which is affecting your ability to form certain sounds.