If I was hospitalised by a medication

[NameChangedAndForgotOldName]

Then I'm allergic to it?
I couldn't breath, needed an ambulance, oxygen 3 days of the mask I can't remember the name of because my oxygen levels kept dropping and 4 days in hospital afterwards. Hospital dr told me not to use it again.

When I was in hospital last time they asked if I was allergic to anything then said that's not allergic, it just aggravated my asthma

An allergy is a response by your immune system - you can have a reaction to a drug without it being an allergy - it may be that the reaction is a known side effect of the drug (worsening of asthma symptoms with. Ibuprofen or diarrhoea with antibiotics for example). So you can say you had a bad reaction to a drug previously and have been told not to take it again but it doesn’t necessarily mean you are allergic to it.

It being an allergy or otherwise doesn’t dictate how severe it is - mildly itchy hives is an allergy, renal failure from taking ibuprofen when dehydrated is a known side effect - an allergy just describes a specific thing

As the others have said, an asthma attack triggered by a medication isn't the same as an allergic reaction. The mechanism that causes the problems isn't the same, and the treatment isn't the same. In your case though, the end result (that you should avoid the medication in the future) is pretty similar.

It's important for your doctor to ask exactly what happened though because there is a lot of public misunderstanding around allergies. If someone says they have an allergy, you can't always take it at face value. For example, a lot of people claim to be allergic to antibiotics like amoxicillin, so then they have to be prescribed alternatives. However what actually happened was that they got diarrhoea when they used it. That's not an allergy, it's a side effect, and doesn't mean they can't safely use the antibiotic. In your case there isn't a lot of difference for you, you just need to remember not to take it in the future, but the distinction could be important to your medical team in the future so it's important that it's properly recorded in your notes.

If it triggered your asthma then its not am allergic reaction no. The treatment you would give for an asthma attack and an allergy are different for example, they are caused by different things.
In future you just say "I can't take x medication, it triggers my asthma" or something like that.