If that was my potted tree, I would remove as much of that soil as possible, rinse the roots off and replace with a fresh bug free soilless mix...)

"brownish shells" sound like scale, not aphids. They can be removed manually and that is one of the best and most thorough methods, although a bit tedious.

If scale - photos of the plant and its visitors would help immensely - it is unlikely these are originating from the soil but removing and examining the roots may be advised.

I agree with garden girl...Unless of course you mean what your your title says..That you saw a bunch of bugs in the roots...

I wonder if you could try mixing some vegetable oil, rubbing alcohol, and dish soap with warm water and spray the tree with that. I can't imagine it would hurt it and it should be similar to horticultural oil....please correct me if I'm wrong guys. I also agree with Mike about replacing them mix although that may require $.

If the shells you see are on the plant then it is quite likely scales. You can take a q-tip and rub them off meticulously. If you have rubbing alcohol then dip the q-tip in that and do the same. You will have to check every few days to get rid of new ones.

Two other things come to my mind if it is on soil: Either they are osmocote like slow release fertilizer shells or they are aphids on your leaves that are moulting and you are seeing their dead tissue. You can ignore the first one. For the second one look for tiny critters usually on young leaves and flower buds.

Although vegetable oil or dish are not as safe as a good hort oil or insecticidal soap you can use it in a pinch. 2 tbsp per gallon and 1 tsp of dish soap per gallon of warm water and shake it well. Then spray while frequently shaking the mix. Try not to get that stuff in the soil as much as possible.

That is how they look so yeah not aphids but scales like you said, since they do not move.

Picking them up with my bare hand is NOT working because the second day they`ll just appear a dozen more and leave that goo stuff EVERYWHERE, it is so sticky.

I really need something to spray the leaves and the bark with so it destroys their honey and of course them.

I`m planning on eating the fruits it makes as I did last year so I dont want to spray something that could potentially affect my health OR my tree`s health.

A couple more pictures above showing a fallen leaf and the tree and how it lost most of its base leaves.

You have scales. The best option is to use a q-tip dipped in rubbing alcohol and rub out scales individually. It will take a while and you have to look carefully along stems and leaves. Under side of leaves especially along the veins are also their favourite spots. The sticky stuff is a sort of honey they produce to attract ants to help in transporting their eggs elsewhere. You can just wash them off.

Inspect your plants every few days to eliminate any new ones. If you keep at it then after a few times they would be gone. But you need to be vigilant since they can reappear. Check other plants too while you are at it.

Neem rocks, and if you want to make the best full use of it, make sure to emulsify it as you are using it so that a nice even layer adheres to the pests and leaves....You can also mix with alcohol even better......

Vladimir: I will have to disagree from various angles. Swiping a q-tip dipped in 70% alcohol across stems or leaves of a single small plant like OPs can be done in less than 10 minutes. And it is very effective. Still has to be done a 2-3 times at 3-4 day intervals just like any other pesticide. That is one application is not going to get rid of scales anyway.

The primary action of neem oil is just like any other oil - suffocate the critters. And it is still going to miss some. Granted it is easier to just spray. There is some research around showing that active ingredient of neem (azadirachtin) interferes with biological functions in plant pests and other small animals - disrupting their life cycle. It has been shown to have some antifungal properties too. And so those can be considered as an added benefits. But the OP wanted a solution without neem oil or purchasing something. I was hoping OP may already have rubbing alcohol ( or for that matter plain old clear drinking alcohol like vodka will also be effective).

To me alcohol is a very effective first line of defence and it can be applied "almost" anytime regardless of condition. The only caveat is very tender leaves can get dehydrated and die or high temperatures can flash vaporize the alcohol making it ineffective.

Sorry I missed that neem was out of the question. I suggest using Laura's concoction.