Work Hassles

I'm having trouble at work and could use some external objectivity from people who get what it's like to think this way.

The main scenarios are

1) I was having trouble with a client, we'd done some custom work for them and it was slightly different to what they'd envisioned, but it did achieve the business goal. I reached a point where I was panicing and said to the client I'm sorry I'm losing my temper let me transfer you, and put him over to the MD (as my line manager was off).  Work doesn't like that I said I was losing my temper but don't seem to understand that I struggle to lie, especially about feelings.

2) My MD came out and publically blamed me for a problem a customer was having, when I'd said to them that it's be a couple of days to get a response from a 3rd party vendor for some insight into a problem

3) My MD came out and demanding to know why we weren't fixing an issue that was the responisibility of another team. I'd answered, got told that it wasn't an answer and had already then replied in a stressed tone that I don't know what else I can do, only to keep getting questioned, so I ended up covering my eyes and screaming.

It's been a long time since I've felt this way at work and acted put but they're saying I'm harming the company, when the real issues are a lot more deep seated and to do with poor internal management.