Learn English – Good English expression for sorting this between ourselves

In English, we use several metaphors to express this feeling which arises from being forbidden to speak.

• pent-up anger, trapped like an animal in a pen
• bottled up anger, trapped like a fluid in a sealed container
• stifled or smothered anger, stopped from healthy flow like a person who is suffocating

Bridle? Maybe. Literally, bridle, n., is the device for controlling a horse's head. Bridle, v., can mean to control a person or to control one's own visible reactions, as a rider controls a horse using a bridle (trans.). Or, it can mean to react with anger (not necessarily hidden) when one's will is interfered with (intrans.). The problem, then, is that bridled anger may be misunderstood to mean the act of bottling up an emotion, when what you meant was the resulting feeling.

Responding to the follow-up question about where we locate stifled anger: emotional reactions are located in the stomach not because of a cultural metaphor but because of a physical cause. Release of the stress hormone cortisol stimulates the body's “fight or flight” systems and disrupts other systems which might compete for resources, notably digestion. Extreme ongoing emotion can even cause evacuation of the digestive tract and bladder (the person may vomit, urinate, and defecate uncontrollably). This is thought to be an adaptation which enhances survival when one's life is threatened by an attacker.

In English, we often describe the experience of cortisol's effects as a visceral feeling, butterflies in the stomach, knot in the stomach, or sinking feeling in the pit of the stomach.

Several emotions can trigger the stress reaction, such as fear, anger, worry, and excitement. In the case of pent-up anger, the stress is continuous because the situation is unresolved, so we are likely to feel a knot in the stomach.

I'd have expected your first option to be far less common than the other two, but a couple of Google Ngrams show that this view is probably unwarranted. Only 'at least' seems to be commonly used, though the other two are not unknown. I'm surprised; I'm quite familiar with 'at the very least' as a pragmatic evaluator.

At least (as a pragmatic marker – mitigating), as you say, has a different meaning, unwanted here.

I'd avoid at the least as sounding unnatural, though there's no grammatical reason why at the very least should be correct and at the least not so.

You could go with at the very least, which sounds a little over the top to me. I'd rephrase to 'It causes at least one problem: ...; it might also cause others.' This usage of 'at least' is as a quantifier rather than a pragmatic marker.