if you look at the data sheet for a tsop4838 you will see that you have a numbers of issues to contend with
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1. @9600baud the bit time is 100uS or approx 4 cycles of 38khz , about 2 to three times faster than the tsop4838 can cope with
2. the max burst rate is 800/sec a 9600baud stream can exceed that
3. after a 70 cycle transmission a 12 cycle min tx gap must be made [some devices can lock up if u don't and need a pwr cycle to recover]
4. the device will do its very best to reject a continuous transmission and go mute till a min tx gap in tx is observed, which is what you are doing.

overall tsop4838 is not particularly suitable for serial tx from a uart, you could try a much lower baud rate and you will need to
invert the transmission logic so that there no transmission at idle

i would also wire tx to rx directly to verify code works before trying ir link, also have a look at Manchester encoding and check out ir tx protocols like RC5/6 NEC etc