Can't reach wp-admin

I’ve been working on the wordpress site locally for a week now, with the custom theme. I was always logged in and had no troubles entering the admin page. I used direct link (localhost/sitename/wp-admin) or went to main page through MAMP and reached dashboard from the top panel.

Today I entered the main page of my site and discovered that I was logged out from admin (top panel wasn’t there). So I typed link manually and got the blank page.

I tried also to enter another site I was working on locally (with another theme) and as this link worked I replaced names in the link where necessary and got to login page. But I can’t log in because I receive an error: “Cookies are blocked due to unexpected output.”

I read some advice here (renamed plugins, turned on debug) but it doesn’t help.

How can I check that the theme is not the case? If I delete it I’ll lose all my work as I understand (I wrote some css in theme settings and created content with visual composer). And maybe there is a possibility that something else is a problem?

Sorry for the long post I tried to describe the problem thoroughly.