Depending on your level and skillset there are several places to go after radahn. The most obvious choice is to take the Grand Lift to Leyndell, which offers immersive NPC storylines and some amazing weapons. However, there are also other great options like Volcano Manor or the ruins of Gael Tunnel.
If you don't want to do any more shardbearer fights, you can skip Caelid and continue your journey in the Elden Ring. Defeating General Radahn in Redmane Castle is a necessary step to progress, though, and he is one of the most challenging bosses in the game.
The fight begins with Radahn shooting extremely fast and overwhelmingly powerful gravity arrows from his greatbow at the player. The best way to avoid these is to just dodge them when they are about to hit, and to stand behind weapon graves or debris if he starts shooting them in front of you. During this phase the player will see golden summon signs spawn on the ground (depending on how far you have progressed in the NPCs' storylines, these may or not include Iron Fist Alexander, Blaidd, Patches, Okina and Lionel the Lionhearted). If the player keeps resummoning them, they will slowly start to whittle down Radahn.
Once the players reaches about half of Radahn's health, he will start summoning meteors that will hit the players and their summons for massive damage. The players can re-summon their allies and hide behind the sand dunes in the arena to protect themselves from these, but it's still important to keep the allies reviving as often as possible.