No, the links do not count at all in the Alexa ranking.
Alexa ranks pages primarily based on actual visits to their pages. If someone who has his toolbar installed visits a page, it counts as a hit. The more unique the hits, the higher they rank you.
What CAN happen is that the number of visits you receive is lower than the previous one, due to your site ranking in Google, Bing and other search engines. There are SEOs who think that getting many links from this type of sites can make your site demoted, while others claim that they have no influence on your site. ranking.
Another factor to take into account is that maybe other sites in your country are improving their rankings and lowering you accordingly.
Some suggestions to help you get started:
- Check the analyzes of your site, the number of visitors you receive,
understand how you get them, your best and worst pages, etc.
- Check your site to see what it looks like in the mobile and desktop versions
- Correct errors with pages in your site and / or your architecture
- Optimize your site for page speed
- Check security on your site
- Learn and apply SEO on your site to increase the number of your visitors in the long run
- Launch a few paid campaigns to increase the number of visitors and thus increase your
Alexa short term ranking.
I hope this helps you!