I get itchy eyes when the weather is nice outside. Does this mean I have allergies?

Maybe. If you get watery-itchy eyes, nasal stuffiness, drainage from the nose, coughing, sneezing.. Then yes you might have allergies. If you get itchy eyes "every-time the weather is nice" - like every spring and fall... You probably have allergies. A way to simply determine is to take any over-the-counter allergy meds: claritin, zyrtec and see if your symptoms go away...
Probably. I assume "nice" weather means sunny and warm, with low humidity. This will favor higher airborne pollen, particulate air content with subsequent affect on the eyes.