It's extremely unwise to jump 3 releases (F20 to F23) via upgrades. For maximum success, do F20->F21, F21->F22, then F22->F23. In fact, you'd best be served by backing up all your stuff and doing a fresh install of F23 (there's been a LOT of changes since F20).
Note also that the upgrade sequence will probably have problems since F20 and F21 are both end-of-lifed and some of the repo mirrors won't have the content any longer. In fact, the Fedora project itself moves the content to http://archives.fedoraproject.org/pub/archive/fedora/linux/releases for end-of-life releases.
Now, as far as your slow downloads, you might try doing this as the root user:
echo "0" >/proc/sys/net/ipv4/tcp_sack
and see if that improves things (depends on how your firewall behaves). If it does, you can make it permanent by adding the following line to either your /etc/sysctl.conf file or create a new /etc/sysctl.d/10-openuptcp.conf file (depends on how old your setup is) and put it in there:
net.ipv4.tcp_sack = 0