First we've got to understand that everybody's body is different. The healing process will differ from person to person but generally the signs and symptoms of a healing navel and an infected navel are pretty much common!
I don’t think I’ve ever gotten an infection up till this point (the first few weeks is when your healing navel is most prone to infection) so I can’t help much with symptoms of an infected navel. I would think the most obvious sign of an infection would be yellowish-green pus and of course, more severe pain. 
It is most important that you do not mix up signs of a healing navel piercing with signs of infection.

DAY 1 AND 2

So the first few days after I’ve got my piercing, my piercing seemed fine, not much redness, swelling or flaking. Of course it would be slightly sore to the touch since it’s a new piercing :)
Everyday, I do salt soaks at least once a day and then wash my piercing with NaCl 0.9% solution (20ml) bought from a local drugstore to wash off any remaining salt. I also spray it with H2Ocean Spray twice a day. The detailed steps will be up in my next post!
Word of caution: my belly area seems pretty hairy so excuse me hahah!

WEEK 1
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Week 1, slight redness a the site of needle entry and exit. It’s a new wound after all!

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Week 1, still no signs of pus or crusties!
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Week 1: slightly red around the piercing site

WEEK 2

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Week 2: The swelling and soreness kicked in! I’ve done a lot of research as I’m honestly pretty paranoid about getting an infection or rejection. I’ve done cross references and yes, a few days after your initial piercing, your piercing site is bound to become red and slightly swollen, so don’t mistake that for an infection.
I still wash my piercing regularly with saline solution after salt soaks and spray it with H2Ocean Spray. but I was afraid that wasn’t enough. 
Usually youtubers or piercers would recommend washing the piercing with antibacterial soap(usually Dial Soap which is not sold in drugstores in Singapore). I was afraid unscented Dettol body wash would be too strong. 
I tried Dettol body wash anyway, but it made the swelling and redness worse for me. I chanced upon this antibacterial foaming wash by a local company called ICM PHARMA. It helps treat and prevent acne and other skin infections. It was definitely milder than Dettol so I continued to wash my piercing with it.
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Week 2: Still red and sore, but no sign of pus or severe pain.
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Week 2: Getting better! Redness and soreness is going down slowly.
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Week 2: Redness and soreness is continuing to go down! Up till this point, I am cleaning my piercing regularly with antibacterial soap (ICM PHARMA) whenever I bathe, saline solution after I do my salt soaks and H2Ocean Spray.
Check out my other post for the detailed steps on cleaning!