Can an iPhone get a virus?

Since last night,when I attempt to open what I know is a legit link in an email, up pops notification my phone has been chosen at random and I have won a fabulous sweepstakes. I cannot make the notification go away, so I end up having to basically shut down and restart. Now, sometimes it is hard just to get onto the Internet on my phone. Coincidence? I fear not. Help, please!

Back up phone. Restore to factory settings, sync phone. Is your phone older? Newest updates on older phones can slow the phone down.

Thank you! Yes, phone is older. But I really like it so would like to keep it until it absolutely has to be replaced.