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There are some games in the Macross series that are shooters where you can alternate between 3 forms including a robot and plane. Not sure if they were ever released on PC though, were you possibly playing an emulator?
Thexder is a good match for the description.
I have to second Thexder. Specifically, Sierra's American-made Windows 95 version, judging by your description of platform and time.
I can all-but-confirm it being Thexder, as I've played it no less than six months ago and have got the CD sitting in one of my drawers.
I've been lurking here for ages, but it's 3am and I have the dumb so if someone could point me to where the pages about formatting posts are that'd be awesome. Anywho you've inspired me to find, and stream, the game assuming I can get it working on this computer. And of course I'd link you to my stream if I knew how.
Edited by TheBigDawg
PC game from the 90s, not sure if I played it on Win95 or Win98.
2D, side-scrolling platform-shooter, you played a robot that could transform into a plane version of itself, and possibly another form as well. There was shooting, but, for the life of me, I can't remember if there was ammo or multiple weapons. The game did require a graphics card though.
I couldn't even tell you what country it's from, but judging from the era and the fact that it's in English, I'm going to go with it being American.