Outoing mail blocked

I'm sending what I'd consider to be a very normal level of emails out - maybe ten an hour - and they are being blocked because I have "too many messages". This is making my work email account completely unusable and I have had to switch to using my personal email to send work emails which is not the best. I will have to move to another email provider if this is not resolved quickly. I emailed about it and was asked to send a screenshot of the problem but have since had no reply.