I would like to do BA Psychology distance education at IGNOU at the same time I would like to do BSC Zoology at St.Thomas college at Thrissur.
You want to pursue one full time bachleor's degree and one distance mode bachelor's degree. It is common now for candidate to have the desire to have additional degrees in a short period to enable them to be better placed for jobs and further career progression. A student can do one full time and maximum one distance mode degree simultaneously. You cannot do two full time degrees at the same time. You can have a copy of this UGC report (https://www.ugc.ac.in/pdfnews/0367166_morethanonedegree.pdf).
As far as BA Psychology is considered (http://www.ignou.ac.in/ignou/aboutignou/school/soss/programmes/detail/404/2), there are no entrance exams, you need the basic 10+2 pass, you can finish the course by 3-6 years.
Please enroll for the BSc Zoology at St.Thomas College, Thrissur, get a grasp of the actual voulme of studies, settle down. Once you are familiar with the course and have the confidence that you can do a distance degree simutenously, please meet the prinicipal and the administration team and inform about the desire. If there are any reservations, please shown them the UGC report.
If you still have issues regarding grant of permission, then write to UGC and ask for guidance. I say this because, rules keep changing and the local college should allow you to take the exam in the stipulated date and it is better to clarify this in writing before you start the second course.