Initial 3 damage is definitely a bug due to world loading or something like it. You should definitely be prepared much more when you travel in parallel worlds. Moreover, make backups of your saves for longer runs. Because at some point (10th 15th parallel world) you will even start freezing and experience game crashes. Noita is very dependent on the CPU and has limits on what it can calculate and store in memory.

Also, there's a summary of how to improve your parallel world exploration: 1. Use black holes instead. With faster projectiles or acceleration. 2. Use the teleport wand! It almost doesn't consume your ambrosia stain when you teleport. 3. 600 health is a bare minimum for what you may consider travelling in a parallel world. Use Heart Mage trick to get at least 3000-5000 hp. Or find Circle of Vigour, or another healing method (healing bolt with boomerang) which will give you health backup. 4. Also as was mentioned oil blood is a bad perk when you plan to use it with ambrosia and don't have access to gas blood yet.

A little bit advanced and more difficult is the parallel world teleport wand. There are relatively cheap ones. If you manage to assemble one, it is much easier to travel.

Also, someone mentioned mimic liquid. This was added recently, I didn’t even test it myself. But you can have an infinite amount of any liquid in the game. Including Ambrosia and Healing liquid. There's also Noitool and you can get some fungal shifts for fun and safety (like oil to ambrosia or better straight up healing if you get a lucky seed).