iOS 8.3 came with many fixes for problems with Wi-Fi. The reason for your issue could also be the router.
Here are a few things that might help you:
After updating, reset your iPhone. This won't remove data or settings. To reset, press and hold Home and Power button simultaneously until the Apple logo appears. Let go of both. Your device will power up on it's own.
Go to Settings - General - Reset and select Reset Network Settings. This will also remove your Wi-Fi and it's password. Set it up again afterwards.
Reset the router. - Turn it off and on again.
Make sure it's software is up to date.
Also, if Johanna's advice doesn't work, if you updated OTA, you could repeat the process through iTunes on your computer, making sure to back up your iPhone first.