You have created what is known as a "network of sites": multiple domains that all inter-link to each other. To some extent, you are right to be worried. Network of sites have been used to spam search engines in the past. Google often penalizes networks of sites as "link schemes."
Google's Matt Cutts has a video where he address the question of whether one person can legitimately own many inter-linked domain names.
Three sites is not a lot so, it's probably not going to be a huge issue but, 30 sites or 300 sites is absolutely the sort of thing where your
competitor or an average user, who is landing on the page is going to be like, "Why are all these different sites cross-linking and what do they really have to do with each other?"
Now, ideally, it might be something like a men's clothing page and a woman's clothing site and a children clothing site. And if they're relevant that's a perfect reason to link those three together. So, if it's under the same corporate umbrella, you know, whether there's a good reason to do it, I don't see that there's any problem at all and it is a relatively small number of websites to be linking. But, bear in mind as you grow and as you grow, if you have a ton of links down at the bottom of your site, a lot of regular users will get turned off by that. And a lot of competitors would be like, "Oh, why is this person cross-linking every single site?" So, a good rule of thumb is sort of asked a regular person off the street, and if they sort of look at it a little bit strangely, then you'll know that you've probably gone just a little bit too far.
nofollow on those links would break apart your network of sites. As far as Google is concerned, each site would be its own separate site not linked to the others.
On the other hand, you won't be penalized if:
- The sites are clearly related
- You use the same brand across all of them
- You don't try to hide your you identity or affiliation with all the sites
- You don't use keyword rich anchor text between the sites
- You link in a way that is not overwhelming to users (for example hidden behind a button, or only on a "related sites" page)
This StackExchange website has links to a ton of other related StackExchange sites in the footer. Their footer links are the type that Matt Cutts called out as being spammy looking and not meant for users. Because the StackExchange sites are high quality and the links are relevant, they get away with it anyway.