There is simply no better way to build a sense of tempo than regular practice with a metronome. While it is still a good idea to purchase a metronome, if you have a computer near where you practice, you can have one for free thanks to the internet.
If you have a microphone on your computer, here’s an online tuner. Don’t just use it at the beginning of your practice session, continually refer to it. This will help you grow more acquainted with the intonation tendencies of your instrument to help you play ALL the notes in tune, not just F and Bb.
TUNING FORK - PITCH REFERENCE
Don’t just practice relying on a tuner to tell you when you’re in tune. Practice your ears as well. This link will play any pitch for you, play along and listen for the pitch to match. If you play a transposing instrument, remember to take that into account when choosing what note to play.