So, I was accepted to three universities for graduate school, one of which is the school at which I'm currently finishing undergrad in aerospace engineering. I received an offer from school A for a GRA position, but wasn't interested in the research topic, so I declined admission there. School B, the one I'm currently attending, offered me a GTA position, and I received an unofficial offer from a professor doing some great research for a GRA position. When I met with said professor, the position sounded like a sure thing. School C, when I contacted them, said they would be unable to offer any funding. With this information, I accepted admission to School B. However, about a week ago the professor I had spoken with informed me that some unexpected financial issues had risen, and he would be re-evaluating his GRA offers to determine whether they were feasible. I have yet to hear his final decision. A couple of days ago, I was contacted by a professor at School C offering to discuss their research for a possible GRA position.
Now, I wholeheartedly believe that it would be best for me to do research from the outset, as my goal is to obtain a Ph.D. However, I'm not sure what the best course of action is. If the first professor informs me he will no longer be able to fund me, that would sway my decision towards attending School C if I was offered a GRA position there instead of taking a GTA position. The problem is that I have already accepted admission here. I'm wondering whether it would be useful to pursue the second offer I received, and, if the first offer falls through, if it would even be possible to "switch" my admission to the other school. Any thoughts?