Why not give the B.Eng/B.Arts double degree a go for a semester? You'll retain your Bachelor of Arts (whilst still making progress) and you can experience a bit of Engineering.
OP doesn't have the pre-reqs to transfer into a B.Eng/B.Arts. Instead he/she could probably do introductory maths/science electives first, and see how it goes.
The prospects in computer and sofeware engineering are decent overall (especially when compared to other streams of engineering where job prospects can be kinda shit), but as with most courses you still need to be good (academics, communication, experience, networks) to experience decent job prospects. There are many average/above average engineering grads (with almost empty resumes) out there struggling for career opportunities (it's still a competitive world out there)
An arts degree is seriously not as bad as people make it out to be, if one is good at it and actively involved in extra-curricular activities. Considering relevant careers for arts grads are writing, media, NGOs, teaching, management consulting (which is pretty lucrative but competitive), politics and academia ( there are probably more, but these are the obvious ones), good communication skills as well as networking/experience is required. Most of the time, it's best to do something you are good at, as no matter how unemployable a field/career may seem (e.g. law- where there is a mass over- production), there will always be some people that find employment in those areas.