Will long term use of Breathe Right nasal strips affect the shape of my nose?
Certainly, it's worth the money to test a box, which is hardly "long term use." You may discover that they don't work.
I have sinus congestion, will nasal strips help me with running?
Definitely, but I must warn you - nasal strips are very addictive. You'll soon realize that you love the 'free breathing' experience and it will get hard not to rely on them.
I would recommend Yoga and basic breathing exercises. It would also help to triangulate the causes for your nasal blockage and work upon them.