First, you need to understand developing new ciphers is really hard. And assuming your work is sufficiently original (rather than a small modification of a well known secure cipher) The odds are overwhelmingly against an amateur creating a secure original cipher. And even if you didn't stray very far from well trodden ground there are still plenty of pitfalls.
Nevertheless, you ask how you get professional attention for your cipher. First is it needs to have a reason to exist. I felt like writing a new cipher isn't good enough to get serious attention, the cipher should solve a real problem. Is it more efficient on particular hardware? Does it have interesting properties making it particularly suitable for some task? etc.
Once We have established it has a reason to exist and should it be proven secure would bring value comes the next step.
Analyze the cipher yourself. There are a bunch of standard techniques to analyze ciphers such as linear and differential cryptanalysis, You need to apply these and show they do not break your cipher and you have a significant safety margin. Also show good avalanche properties, perhaps black box statistical tests etc.
After you have done this it was written up your work it is evident you have something potentially valuable and there is a non-negligible chance of it being secure. Then you can show it around, and try to get serious people to spend effort on your cipher.
