Aren't we most likely subject to artificial selection?

Let's make a nuanced distinction between selection criteria and the adaptation due to selective pressures. 'Selection criteria' are the constraints that the environment (including human agency) place on an organism; the better an organism adapts to the selection criteria, the more likely it is to survive and breed offspring, and the more likely its genes will be passed to future generations. However, the process of adapting to selection criteria is open-ended different individuals within a species (not to mention different species) might follow different paths of adaptation, and the outcome is organic and unpredictable, except that it ought to increase the overall fitness of the species as a whole. Further, the more restrictive the selection criteria, the more limited the organisms gene pool, and the less fit the species becomes as a whole. Generally speaking, a healthy species has a diversified gene pool that it can draw on to adapt as environments change; mutts are generally healthier than purebreds, if you'll excuse the dog analogy.

Artificial selection means little more than artificially imposing selection criteria. It does not affect the process of adaptation at all, except to weed out those creatures that follow undesirable adaptation paths. We've applied this process to a number of animal species with mixed results — E.g., the modern commercial turkey, which has been bred into a form that effectively guarantees its extinction outside of a human farm — but there have been very few efforts to apply artificial selection criteria to human beings. The few times that effort has been undertaken consciously it has proved universally horrifying: eugenics, ethnic cleansing, genocide, racial segregation and anti-miscegenation laws, etc. As humans we lack the wisdom and knowledge to determine and apply ethical and effective criteria for selection on our own species.

It may be tempting to think that we intelligently control our environment, but an objective analysis of our species' fitness — considering the extent to which our waste products are building up in the soil, water, and atmosphere — seems fairly dismal. If there is an intelligent designer who has been applying selective criteria in order to guide adaptation, then we probably need to embrace the idea that the human species is not the desired end-form, and pressures are being applied to bring out the characteristics of some current or future species. If there is no intelligent designer, then we are merely poisoning ourselves in our own unconscious reactivity.

No, the process parents use to select their partners to produce children is not coordinated to change the gene pool of all humanity persistently. So there is no artificial selection happening. Though the Holocaust would be an example of an attempt for something similar, just to give an idea of what artificial selection could look like.

Note artificial selection and artificial selective pressures are independent concepts, and "intelligent design" typically means the absence of any selection. So the terms used in the question are confusing.

Since most animals on earth are artificially selected for by humans

Evolution works over many millenia, hence its important to think of a time framing. If one was to think of the current epoch, then your phrasing would be right, and this is why the Anthropocene is being considered currntly by International Geological Congress as an epoch of geological time; however, when we consider the whole fullness of time where life has existed on earth, then of course most life have not been subjected to dirct selection pressure by human.

At bottom, all selection pressure is natural. The distinction between artifical and natural is itself an artifical one. Consider a bird, it builds a nest as a home, we do not consider the nest as somehow un-natural to the bird and to nature; they are both natural. However, when come to the urban environment, it's often considered artificial, and to be put against nature itself. Yet it is natural to the human animal to build its habitat as ants do theirs, as do beavers or the very birds.

Does this imply you're a product of intelligent design?

There's no proper argument made, so one can't consider the implication made here.