I'm 22female. 5'8, 108lbs. No medical problems & nursing mom. I have trouble gaining weight. Do I need supplements or vitamins? I want to gain lbs.

Maybe. Your bmi (body mass index) is the the underweight category. If you are healthy I would suggest you get a nutritional consult to evaluate the caloric and nutritional content of your average daily diet. In the meantime you certainly can take a nutritional supplement like ensure to add healthy calories and nutrients.
Waiting on Weight. Choose a good protein supplement. Whey, casein and soy are good sources. Whey is more rapidly absorbed than casein. Soy is plant based and has isoflavones which mimic some female hormones. Choose a concentrate not an isolate to avoid degraded protein in the manufacturing process. High protein intake with essential fats from pistachios, almonds and walnuts will bulk you up while nursing.