Well if Wikipedia is to be believed, yes they can be transmitted by mosquito, but what's more troubling is that you have one, from what I saw, if you do the vasoline thing, you still need to have a medical pro remove it, or risk it rupturing if you try to just squeeze it out. The risk in rupturing is that some people go into severe anaphylactic shock. Per the mosquitos (from Wiki): "Botflies deposit eggs on a host, or sometimes use an intermediate vector such as the common housefly, mosquitoes, and, in the case of Dermatobia hominis, a species of tick. They are common in Belize. The smaller fly is firmly held by the botfly female and rotated to a position where the botfly attaches some 30 eggs to the body under the wings."
https://en.wikipedia.org/wiki/Botfly. I've had success before controlling mosquitos in my
yard by brewing up a batch of hot pepper-garlic spray, and liberally dousing all the grass and shrubs, but it might irritate
cattle if sprayed directly on their skin. My mix: couple of habeneros, whole head of garlic, plain non-toxic dish soap (small amount), 1/4 cup veg oil, and
water to fill a handheld sprayer. Steep in hot weather for a day or 2 and then strain out the solids, spray everything.