A thesis is normally something that you do in order to earn a certain degree (e.g. a Bachelor's, Master's, or a Ph.D. thesis). What you are describing would probably be called a (working) paper or a manuscript.
Yes, you can submit your paper, once it is finished, to a journal in your area. Whether you are enrolled in a biology programme or a computing programme or in no programme at all has no bearing on this. There is also no formal requirement that you need anyone else (such as a professor) to be a co-author. Indeed, someone who did put in the work to earn this should not be a co-author of your paper.
If you paper is in biology, it seems unlikely that a professor at the computing (computer science?) department would be able to help with the substance of the paper, unless it also touches on their area of expertise. However, you could certainly reach out to a professor you have a good relationship with and ask them questions about how the mechanics of publication works. The disadvantage of asking a computer scientist would be that they are probably not familiar with how publishing works in biology, but they could perhaps give you some general advice. An advantage would be that it is unlikely that they would try to convince you to add them as a co-author.
However, while there is nothing preventing you from trying to publish your work on your own, beware that publishing your first paper without any outside advice is a very difficult task. In particular, you may not be fully aware of what the expectations are as regards the structure a paper, methodology, relation to the existing literature and so on. I would considering reaching out to an expert in the area at your university and discuss the matter with them. The danger that they will steal your work is, I believe, minimal. (At least according to my experience with Western academia, I don't know how things work elsewhere.) On the other hand, they might wish to be a co-author on your paper in exchange for their assistance. Whether or not this would be a good deal for you is difficult to tell, since it is difficult to estimate (if you have no experience with academic publishing) how far you paper in its current form is from being publishable. It may be that your paper is publishable as is, but it may also be that the paper requires substantial further work before it conforms to the expectations that people in your target field have of publishable papers, in which case I would think having someone knowledgeable help you with this would probably be a good deal.
Another possible scenario is that they will tell you that you work is not publishable for some reason, perhaps due to a lack of novelty or due to some methodological flaws. If this happens, do not take this too badly: already doing non-trivial scientific work on your own as a high school graduate is something that most people never take the initiative to do, regardless of whether or not you succeed publishing it in a journal (a non-trivial task even for people several rungs higher than yourself on the educational ladder!).