I've received an invoice for an amount higher than the allowance or the upper limit but I have not received an alert message. Is that normal ?

That can be normal.

It could be that your operator is unable to calculate the costs for your consumption immediately.  

In borderline cases or at the end of the month it is possible that you are charged an amount just exceeding the upper limit chosen by you or the standard upper limit without having received an alert message. For instance 50,43 euros instead of the upper limit of 50 euros.

It is also possible that the alert message was not addressed to you as the end-user but to the person paying the invoice (for instance your employer or parents). Or vice versa. Operators are free to alert the person of their choice.  

It is also possible that you have received a high bill due to the use of services by means of premium numbers or text messages and that your operator has chosen not to include calls to these numbers in the general alert system.

However, if you think something is not right, you can inform Telecommunications Ombudsman Service.