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Some pointers to the literature:

For q-SO(3)

If I am not mistaken, $SO(2)\approx U(1)$ has no nontrivial quantum deformation, but $SO(3)$ does; this is explicitly constructed in:

Symmetries of quantum spaces. Subgroups and quotient spaces of quantum SU(2) and SO(3) groups, P. Podles (1994)

Quantum SO(3) groups, P.M. Soltan (2008)

For q-Sp(2):q-Sp(2), see Section 3.2 of

Noncommutative families of instantons, G. Landi et al. (2008) [Section 3.2]2008).

More general references on quantum classical groups:

Quantum deformation of classical groups, T. Hayashi (1992)

Quantum symmetric spaces and related q-orthogonal polynomials, M. Noumi and T. Sugitani (1995)

Orthogonal and symplectic quantum matrix algebras and Cayley-Hamilton theorem for them, O. Ogievetsky and P. Pyatov (2005)
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Some pointers to the literature:

For q-SO(3):

Symmetries of quantum spaces. Subgroups and quotient spaces of quantum SU(2) and SO(3) groups, that you may or may not find helpfulP. Podles (1994)

Quantum SO(3) groups, P.M. Soltan (2008)

For q-Sp(2):

Noncommutative families of instantons, G. Landi et al. (2008) [Section 3.2]

More general references on quantum classical groups:

Quantum deformation of classical groups, T. Hayashi (1992)

Quantum symmetric spaces and related q-orthogonal polynomials, M. Noumi and T. Sugitani (1995)

Orthogonal and symplectic quantum matrix algebras and Cayley-Hamilton theorem for them, O. Ogievetsky and P. Pyatov (2005)

Noncommutative families of instantons, G. Landi et al. (2008) [$q-Sp(2)$ is explicitly considered in Section 3.2]
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Some pointers to the literature, that you may or may not find helpful:

Quantum deformation of classical groups, T. Hayashi (1992)

Quantum symmetric spaces and related q-orthogonal polynomials, M. Noumi and T. Sugitani (1995)

Orthogonal and symplectic quantum matrix algebras and Cayley-Hamilton theorem for them, O. Ogievetsky and P. Pyatov (2005)

Noncommutative families of instantons, G. Landi et al. (2008) [$q-Sp(2)$ is explicitly considered in Section 3.2]
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